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
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
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
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
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
文摘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.
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘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.
基金the Natural Science Foundation of Henan University。
文摘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.
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.41941017 and U1702241).
文摘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.
