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Isometric Immersions of Lightlike Warped Product Manifolds
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作者 Domitien Ndayirukiye Cyriaque Atindogbe Gilbert Nibaruta 《Journal of Applied Mathematics and Physics》 2024年第7期2490-2505,共16页
In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ... In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions. 展开更多
关键词 Lightlike Warped Product manifolds Globally Null Warped Products manifolds Lightlike Warped Product Isometric Immersions
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A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS
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作者 高雅 毛井 吴传喜 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期474-483,共10页
In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece... In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation. 展开更多
关键词 mean curvature flow spacelike graphs translating spacelike graphs maximal spacelike graphs constant mean curvature Lorentz manifolds
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Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning
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作者 Yongqiang Liu Jianping Chen +3 位作者 Fujun Zhou Jiewei Zhan Wanglai Xu Jianhua Yan 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第8期2996-3013,共18页
Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural informa... Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements. 展开更多
关键词 Homogeneous domain Geological domain Geotechnical domain Structural domain Topological manifold Deep learning
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SOME CONVERGENCE PROBLEMS REGARDING THE FRACTIONAL SCHRODINGER PROPAGATOR ON NONCOMPACT MANIFOLDS
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作者 潘亚丽 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2309-2319,共11页
Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f... Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds. 展开更多
关键词 Schrodinger propagator noncompact manifolds SPECTRA
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On Some Recent Progress in Complex Geometry-the Area Related to Homogeneous Manifolds 被引量:1
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作者 GUAN Daniel 《Chinese Quarterly Journal of Mathematics》 2020年第2期111-144,共34页
In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we e... In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex Homogeneous Space.Together with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests. 展开更多
关键词 Invariant structure Homogeneous space Complex torus bundles Hermitian manifolds Reductive Lie group Compact manifolds Ricci form Locally conformal Kahler manifolds
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HOLOMORPHIC MANIFOLDS ON LOCALLY CONVEX SPACES
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作者 Tsoy-Wo Ma 《Analysis in Theory and Applications》 2005年第4期339-358,共20页
Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard to... Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments. 展开更多
关键词 Holomorphic manifolds infinite dimensional manifolds complex manifolds
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Two-Dimensional Manifolds with Computation V-Function of ODE Systems
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作者 Suqi Ma Bohan Ma Xinping Wang 《International Journal of Modern Nonlinear Theory and Application》 2023年第4期99-106,共8页
The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is comp... The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too. 展开更多
关键词 Stable Manifold Unstable Manifold V-Function Attraction Boundary
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油轮Manifolds及附属设备常见问题24问
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作者 宋红专 《中国水运》 2023年第11期43-45,共3页
在油轮的生产运营中,从初始的商务揽货问卷,填写Manifolds(货油管管头)及附属设备的相关参数;到靠泊前与码头的交换其参数;靠泊后接管和试压及完成货油的装卸;及随后的拆管,都少不了Manifolds及附属设备这个环节。
关键词 Manifold(管头) Reducer(变径接头) Spool Piece(连接短管) 附属设备
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Lower-Dimensional Volumes and Kastler-Kalau-Walze Type Theorem for Manifolds with Boundary 被引量:3
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作者 王勇 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第7期38-42,共5页
In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe ... In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case. 展开更多
关键词 lower-dimensional volumes noncommutative residue for manifolds with boundary gravitationalaction for manifolds with boundary
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Biharmonic product maps between doubly warped product manifolds
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作者 韩英波 《Journal of Southeast University(English Edition)》 EI CAS 2010年第3期502-504,共3页
The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant sol... The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ(dφ(grad(lnb)))+n/2 grad|dφ(grad(lnb))|2=0 and f is a non-constant solution of -1/b2Jψ(dψ(grad(lnf)))+m/2grad|dψ(grad(lnf))|2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps. 展开更多
关键词 biharmonic map product map doubly warped product manifolds
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Generalized Contact Manifolds
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作者 徐旭峰 孙振祖 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第4期25-29, ,共5页
We study a Riemannian manifolds M with a f-structures. If the tangent bundle of the Riemannian manifolds is TM=DD⊥ dimD=2P,dimD⊥=q=n-2p≥1. We can define a generalized contact manifolds, get some property of it.
关键词 Riemannian manifolds contact manifolds killing vector field fstructures
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Totally Umbilical Screen Transversal Lightlike Submanifolds of Semi-Riemannian Product Manifolds
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作者 S. M. Khursheed Haider Advin Maseih Mamta Thakur 《Advances in Pure Mathematics》 2012年第4期285-290,共6页
We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radic... We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold. 展开更多
关键词 Semi-Riemannian PRODUCT manifolds Lightlike SUBmanifolds Totally UMBILICAL Radical ST-Lightlike SUBmanifolds Totally UMBILICAL ST-Anti-Invariant Lightlike SUBmanifolds
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Geodesic Lightlike Submanifolds of Indefinite Sasakian Manifolds
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作者 Junhong Dong Ximin Liu 《Advances in Pure Mathematics》 2011年第6期378-383,共6页
In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, m... In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained. 展开更多
关键词 CR-Lightlike SUBmanifolds Sasakian manifolds Totally GEODESIC SUBmanifolds
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Hamiltonian Mechanics Systems on Three-Dimensional Almost Kenmotsu Manifolds
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作者 Ibrahim Yousif Ibrahim Abad Alrhman Gebreel Mohammed Khur Baba Gebreel 《Journal of Mathematics and System Science》 2020年第2期45-47,共3页
In this study,we concluded the Hamiltonian equations on(M3,φ,ξ,η,g𝑔),being a model.Finally introduce,some geometrical and physical results on the related mechanic systems have been discussed.
关键词 Kenmotsu manifolds three-dimensional Almost Kenmotsu manifolds Hamiltonian mechanics systems.
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Singular Points, Closed Orbits, Stable Manifolds and Unstable Manifolds of Second Order Autonomous Birkhoff Systems 被引量:1
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作者 陈向炜 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1998年第4期330-336,共7页
Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ... Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained. 展开更多
关键词 Birkhoff system singular point closed orbit stable manifold unstable manifold
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THE ∂∂^(-)-BOCHNER FORMULAS FOR HOLOMORPHIC MAPPINGS BETWEEN HERMITIAN MANIFOLDS AND THEIR APPLICATIONS 被引量:2
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作者 Kai TANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第5期1659-1669,共11页
In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we... In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive(resp.non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive(resp.negative)real bisectional curvature.These theorems generalize the results[5,6]proved recently by L.Ni on Kähler manifolds to Hermitian manifolds.We also derive an integral inequality for a holomorphic map between Hermitian manifolds. 展开更多
关键词 Schwarz lemmas Bochner formulas holomorphic map Hermitian manifolds ℓ-second Ricci curvature
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KOPPELMAN-LERAY FORMULA ON COMPLEX MANIFOLDS 被引量:1
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作者 钟同德 《Acta Mathematica Scientia》 SCIE CSCD 1995年第1期90-94,共5页
The Koppelman-Leray formula on complex manifolds is obtained, and under suitable condition the continuous solution of partial derivative-equation on complex manifolds is obtained.
关键词 COMPLEX manifolds CHERN FORM KOPPELMAN-LERAY FORMULA PARTIAL-DERIVATIVE-EQUATION
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GEOMETRIC INEQUALITIES FOR CERTAIN SUBMANIFOLDS IN A PINCHED RIEMANNIAN MANIFOLD 被引量:1
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作者 谢纳庆 许洪伟 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期611-618,共8页
This article gives some geometric inequalities for a submanifold with parallel second fundamental form in a pinched Riemannian manifold and the distribution for the square norm of its second fundamental form.
关键词 SUBmanifolds second fundamental form pinched Riemannian manifold
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A Family of the Exponential Attractors and the Inertial Manifolds for a Class of Generalized Kirchhoff Equations 被引量:4
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作者 Guoguang Lin Lujiao Yang 《Journal of Applied Mathematics and Physics》 2021年第10期2399-2413,共15页
In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Ki... In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained. 展开更多
关键词 Kirchhoff-Type Equation Spectral Interval Condition A Family of the Exponential Attractors A Family of the Inertial manifolds
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Inertial Manifolds for 2D Generalized MHD System 被引量:2
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作者 Zhaoqin Yuan Liang Guo Guoguang Lin 《International Journal of Modern Nonlinear Theory and Application》 2015年第3期190-203,共14页
In this paper, we prove the existence of inertial manifolds for 2D generalized MHD system under the spectral gap condition.
关键词 MHD SYSTEM SPECTRAL GAP INERTIAL manifolds
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