In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean sp...In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.展开更多
The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics...The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential展开更多
Some Liouville type theorems for harmonic maps from Kahler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (except <sub>IV</sub>（2）) to any Riemann...Some Liouville type theorems for harmonic maps from Kahler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (except <sub>IV</sub>（2）) to any Riemannian manifold with finite energy has to be constant.展开更多
Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then t...Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton＇s equations was obtained, and so on.展开更多
Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so o...Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.展开更多
In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is ...In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is at least half of the real dimension. The authors also give a brief proof of a generalized Yau＇s theorem.展开更多
Let f be a holomorphic immersion which maps a Kahler manifold into a Kahler manifold of the same dimension. A Schwarzian derivative Sf of f is proposed. It is proved that: i) if Sf=0 and Sg=0, then Sf·g=0; ii) if...Let f be a holomorphic immersion which maps a Kahler manifold into a Kahler manifold of the same dimension. A Schwarzian derivative Sf of f is proposed. It is proved that: i) if Sf=0 and Sg=0, then Sf·g=0; ii) if the ’real part of the Schwarzian derivative of f on a convex domain in the Kaler manifold is bounded above, then F is an embedding. The upper bound is related to the holomorphic sectional curvature of the domain. This second theorem is an extension of Nehari’s criterion of univalence.展开更多
1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex str...1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex structure. G<sub>2</sub>（TS<sup>4</sup>） is called （1, 2）-symplectic if the （1, 2）part of dk is zero where k is the K（?）hler form of G<sub>2</sub>（TS<sup>4</sup>）. In this note, we prove the following theorem:展开更多
In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.
In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.
In this note. we will show that no nonuniform lattice of SO(3, 1) can be the fundamental group of a quasi-compact Khler manifold. Thus, combining with the result in [1]. one gets that a nonuniform lattice in SO(n, 1)(...In this note. we will show that no nonuniform lattice of SO(3, 1) can be the fundamental group of a quasi-compact Khler manifold. Thus, combining with the result in [1]. one gets that a nonuniform lattice in SO(n, 1)(n≥3) cannot be π_1 of any quasi-compact Khlerian manifold.展开更多
Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove...Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E’=E|<sub> \D</sub> compatible with the parabolic structure, whose curvature is square integrable.展开更多
基金National Key Basic Research Fund (Grant Nos. G1999075109 and G1999075107) the National Science Fund for Distinguished Young Scholars (Grant No. 10025104).
文摘In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.
文摘The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential
文摘Some Liouville type theorems for harmonic maps from Kahler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (except <sub>IV</sub>（2）) to any Riemannian manifold with finite energy has to be constant.
文摘Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton＇s equations was obtained, and so on.
文摘Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.
基金Supported by NSFC (10401042)Foundation of Department of Education of Zhejiang Province.
文摘In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is at least half of the real dimension. The authors also give a brief proof of a generalized Yau＇s theorem.
基金the National Natural Science Foundation of China
文摘Let f be a holomorphic immersion which maps a Kahler manifold into a Kahler manifold of the same dimension. A Schwarzian derivative Sf of f is proposed. It is proved that: i) if Sf=0 and Sg=0, then Sf·g=0; ii) if the ’real part of the Schwarzian derivative of f on a convex domain in the Kaler manifold is bounded above, then F is an embedding. The upper bound is related to the holomorphic sectional curvature of the domain. This second theorem is an extension of Nehari’s criterion of univalence.
文摘1. Let S<sup>4</sup> be a four-sphere and let G<sub>2</sub>（TS<sup>4</sup>） be the Grassmann bundle on S<sup>4</sup> with natural Riemann metric and almost complex structure. G<sub>2</sub>（TS<sup>4</sup>） is called （1, 2）-symplectic if the （1, 2）part of dk is zero where k is the K（?）hler form of G<sub>2</sub>（TS<sup>4</sup>）. In this note, we prove the following theorem:
文摘In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
基金The NSF(11101352) of ChinaNew Century Talent Project of Yangzhou University,Fund of Jiangsu University of Technology(KYY 13005)Qing Lan Project
文摘In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.
文摘In this note, we will prove a Kahler version of Cheeger-Gromoll-Perelman＇s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.
基金The author is supported partially by NSF of China (19801026, 10171077)
文摘In this note. we will show that no nonuniform lattice of SO(3, 1) can be the fundamental group of a quasi-compact Khler manifold. Thus, combining with the result in [1]. one gets that a nonuniform lattice in SO(n, 1)(n≥3) cannot be π_1 of any quasi-compact Khlerian manifold.
文摘Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E’=E|<sub> \D</sub> compatible with the parabolic structure, whose curvature is square integrable.
文摘杂化弦的共形不变性和超共形不变性可用圈和超圈的微分同胚群 DiffS^1和Super-DiffS^1描述.基圈的重参数化形成商空间 M=DiffS^1/S^1和N=Super—DiffS^1/S^1.它们是无限维的 Kahler 流形和超 Kahler 流形.本文研究这些无限维流形的全纯几何.用陪集空间的技术讨论了它们的辛结构,通过在 M 和 N 上引入全纯坐标和夏结构我们计算了在原点邻域内的 Killing 矢量,给出了 M 和 N 上的Riemann 度规.这些结果在研究杂化弦的共形反常时有用.
