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L^(2) EXTENSIONS WITH SINGULAR METRICS ON K?HLER MANIFOLDS
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作者 Xiangyu ZHOU Langfeng ZHU 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期2021-2038,共18页
In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles ... In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs. 展开更多
关键词 singular metric optimal L^(2)extension theorem strong openness of multiplier ideal sheaf generalized Siu’s lemma weakly pseudoconvex kähler manifold
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具有处处非零Killing向量场的nearly Khler流形 被引量:1
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作者 张留伟 李兴校 贾志刚 《河南师范大学学报(自然科学版)》 CAS CSCD 北大核心 2010年第4期33-35,共3页
研究了在nearly Khler流形上某种处处非零Killing向量场的存在性与流形的拓扑和几何之间的联系.并且得到了下面的主要结论及其推论:设(M2n,g,J)是一个2n维的近复流形.如果在M上存在一个处处非零的Killing向量场ξ,使得ξ*∧Jξ*是闭2... 研究了在nearly Khler流形上某种处处非零Killing向量场的存在性与流形的拓扑和几何之间的联系.并且得到了下面的主要结论及其推论:设(M2n,g,J)是一个2n维的近复流形.如果在M上存在一个处处非零的Killing向量场ξ,使得ξ*∧Jξ*是闭2次形式,则M局部微分同胚于M1×M2,其中M1和M2分别是分布V∶=span{ξ,Jξ}和分布H:=span{ξ,Jξ}⊥的极大积分子流形. 展开更多
关键词 NEARLY khler流形 kILLING向量场 闭2次形式
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Khler流形上的典型线丛
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作者 詹华税 叶芳草 《集美大学学报(自然科学版)》 CAS 北大核心 2000年第1期1-6,共6页
讨论了Riemann流形上指标形式与共轭点的关系;证明了具非负Ricci曲率的无共轭点Kshler流形上的典型线丛之曲率为零.
关键词 黎曼流形 共轭点 kAhler流形 典型线丛
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Khler流形的几个判定定理
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作者 杨永举 《南阳师范学院学报》 CAS 2010年第12期9-11,共3页
利用Khler流形的有关理论知识,证明了满足共形数量曲率张量与数量曲率张量之差为定号的条件下,紧致的局部共形Khler流形在黎曼联络条件下一定是流形,并由此得出判断Khler流形的两种具体方法.
关键词 局部共形khler流形 khler流形 共形数量曲率
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Kahler流形上的Lagrange向量场
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作者 张荣业 《应用数学和力学》 CSCD 北大核心 1996年第9期849-855,共7页
本文中.我们讨论Kahler流形上的Lagrange向量场,并用它来描述和解决Khler流形上的Newton力学和Lagrange力学中的一些问题.
关键词 张量积 Lagrange向量场 kAEhler流形 牛顿力学
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极小子流形与Khler复子流形的整体性质
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作者 吴金文 徐沈新 《长沙电力学院学报(自然科学版)》 2002年第2期12-14,共3页
利用数量曲率 ,对实流形的极小子流形和K hler流形的紧致复子流形进行了研究 ,得出了它们的一些整体性质 .
关键词 数量曲率 紧致极小子流形 全纯截面曲率 实流形 kaehler复子流形 极小子流形 整体性质
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Khler流形的若干判定定理
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作者 杨永举 《南阳理工学院学报》 2010年第4期98-100,共3页
利用Khler流形的有关理论知识,证明了3个结论:局部共形Khler流形为Khler流形的若干等价条件;满足一定条件的曲率张量的局部共形Khler流形一定是Khler流形;判定Khler流形的两种具体方法。
关键词 局部共形khler流形 khler流形 共形数量曲率 数量曲率 lee形式
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Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds
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作者 Qi’an Guan Zhitong Mi Zheng Yuan 《Science China Mathematics》 SCIE CSCD 2024年第7期1665-1718,共54页
In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the ... In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules. 展开更多
关键词 minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex k?hler manifold
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Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model 被引量:1
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作者 L. Marek-Crnjac1], M. S. El Naschie2] 《Applied Mathematics》 2013年第11期22-29,共8页
The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type.... The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type. Subsequently this analogy is used to deduce the ordinary energy of the quantum particle and the dark energy of the quantum wave. The results agree completely with cosmological measurements. Even more surprisingly the sum of both energy expressions turned out to be exactly equal to Einstein’s iconic formula E = mc2. Consequently Einstein’s formula makes no distinction between ordinary and dark energy. 展开更多
关键词 Hausdorff Dimension Cantor Set Dark Energy k?hler manifold Quantum Entanglement Veneziano Model
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Schwarz lemma from a Kähler manifold into a complex Finsler manifold
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作者 Jun Nie Chunping Zhong 《Science China Mathematics》 SCIE CSCD 2022年第8期1661-1678,共18页
Suppose that M is a complete Kähler manifold such that its holomorphic sectional curvature is bounded from below by a constant and its radial sectional curvature is also bounded from below.Suppose that N is a str... Suppose that M is a complete Kähler manifold such that its holomorphic sectional curvature is bounded from below by a constant and its radial sectional curvature is also bounded from below.Suppose that N is a strongly pseudoconvex complex Finsler manifold such that its holomorphic sectional curvature is bounded from above by a negative constant.In this paper,we establish a Schwarz lemma for holomorphic mappings f from M into N.As applications,we obtain a Liouville type rigidity result for holomorphic mappings f from M into N,as well as a rigidity theorem for bimeromorphic mappings from a compact complex manifold into a compact complex Finsler manifold. 展开更多
关键词 Schwarz lemma kähler manifold complex Finsler manifold holomorphic sectional curvature
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Remark on the Off-Diagonal Expansion of the Bergman Kernel on Compact Kähler Manifolds
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作者 Xiaonan Ma George Marinescu 《Communications in Mathematics and Statistics》 SCIE 2013年第1期37-41,共5页
In this short note,we compare our previous work on the off-diagonal expansion of the Bergman kernel and the preprint of Lu-Shiffman(arXiv:1301.2166).In particular,we note that the vanishing of the coefficient of p−1/2... In this short note,we compare our previous work on the off-diagonal expansion of the Bergman kernel and the preprint of Lu-Shiffman(arXiv:1301.2166).In particular,we note that the vanishing of the coefficient of p−1/2 is implicitly contained in Dai-Liu-Ma’s work(J.Differ.Geom.72(1),1-41,2006)and was explicitly stated in our book(Holomorphic Morse inequalities and Bergman kernels.Progress in Math.,vol.254,2007). 展开更多
关键词 kähler manifold Bergman kernel of a positive line bundle
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关于Vaisman流形的几个判定定理 被引量:1
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作者 杨永举 廖冬 《南阳师范学院学报》 CAS 2012年第6期15-17,共3页
利用Bochner公式和局部共形Khler流形理论知识,主要证明了满足某些条件的局部共形Khler流形一定为Vaisman流形.如:具有非负Ricci曲率且∫m(▽Bω)(B)*1=0;具有非负Rrcci曲率且dim(H1(M))=1等.同时,文中也给出一个判断非Vaisman流形... 利用Bochner公式和局部共形Khler流形理论知识,主要证明了满足某些条件的局部共形Khler流形一定为Vaisman流形.如:具有非负Ricci曲率且∫m(▽Bω)(B)*1=0;具有非负Rrcci曲率且dim(H1(M))=1等.同时,文中也给出一个判断非Vaisman流形的充分条件。 展开更多
关键词 局部共形khler流形 Vaisman流形 Lee形式
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拟多次调和函数的延拓
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作者 宁家福 汪志威 周向宇 《数学理论与应用》 2021年第3期1-12,共12页
本文是(拟)多次调和函数从子复流形延拓的综述.我们先阐述斯坦流形上多次调和函数的延拓,再阐述紧复流形上拟多次调和函数的延拓,其中包含本文作者首次发表的一些新结果.
关键词 斯坦流形 多次调和函数 凯勒流形 延拓
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Completing Einstein’s Spacetime 被引量:3
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作者 M. S. El Naschie 《Journal of Modern Physics》 2016年第15期1972-1994,共24页
The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacet... The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here. 展开更多
关键词 E-INFINITY Cantorian Spacetime SELF-SIMILARITY M-THEORY kaluza-klein Space Fuzzy kähler manifolds Continued Fraction Isomorphic Length Geometrical Gauge Invariance
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Boundary Points,Minimal L^(2)Integrals and Concavity PropertyⅢ—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces
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作者 Qi An GUAN Zhi Tong MI Zheng YUAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第9期2091-2152,共62页
In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified version.As... In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified version.As applications,we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces. 展开更多
关键词 Minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex kähler manifold
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Schrdinger flow of maps into symplectic manifolds 被引量:10
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作者 丁伟岳 王友德 《Science China Mathematics》 SCIE 1998年第7期746-755,共10页
The definition of Schrdinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrdinger flow of maps into S 2, and that there exists a unique local smooth solution for the initial va... The definition of Schrdinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrdinger flow of maps into S 2, and that there exists a unique local smooth solution for the initial value problem of one dimensional Schrdinger flow of maps into Khler manifolds. In case the targets are Khler manifolds with constant curvature, it is proved that one dimensional Schrdinger flow admits a unique global smooth solution. 展开更多
关键词 SCHR dinger FLOW k hler manifold CONSERVATIVE law sectional curvature.
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