共查询到20条相似文献,搜索用时 31 毫秒
1.
《数学物理学报(B辑英文版)》2014,(3)
In this note, we will prove a Khler version of Cheeger-Gromoll-Perelman's soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point. 相似文献
2.
By using the Chern-Finsler connection and complex Finsler metric,the Bochner technique on strong Khler-Finsler manifolds is studied.For a strong Khler-Finsler manifold M,the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈ M-=T 1,0M\o(M),and then the horizontal Laplace operator H for diffierential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor,and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined.Finally,we get a Bochner vanishing theorem for diffierential forms on PTM.Moreover,the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained 相似文献
3.
YAN RongMu 《中国科学 数学(英文版)》2012,(4):727-734
The purpose of the present paper is to investigate affinely equivalent Khler-Finsler metrics on a complex manifold.We give two facts (1) Projectively equivalent Khler-Finsler metrics must be affinely equivalent;(2) a Khler-Finsler metric is a Khler-Berwald metric if and only if it is affinely equivalent to a Khler metric.Furthermore,we give a formula to describe the affine equivalence of two weakly Khler-Finsler metrics. 相似文献
4.
Chao Xu 《中国科学 数学(英文版)》2010,53(11):3027-3036
In this paper, the author has considered the hyperbolic Khler-Ricci flow introduced by Kong and Liu, that is, the hyperbolic version of the famous Khler-Ricci flow. The author has explained the derivation of the equation and calculated the evolutions of various quantities associated with the equation including the curvatures. Particularly on Calabi-Yau manifolds, the equation can be simplifled to a scalar hyperbolic Monge-Ampère equation which is the hyperbolic version of the corresponding one in Khler-Ricci flow. 相似文献
5.
YI Li 《中国科学 数学(英文版)》2014,57(1):9-30
We prove two extension theorems of Ohsawa-Takegoshi type on compact Khler manifolds.In our proof,there are many complications arising from the regularization process of quasi-psh functions on compact Khler manifolds,and unfortunately we only obtain particular cases of the expected result.We remark that the two special cases we proved are natural,since they occur in many situations.We hope that the new techniques we develop here will allow us to obtain the general extension result of Ohsawa-Takegoshi type on compact Khler manifolds in a near future. 相似文献
6.
In this paper, we show the relation between the existence of twisted conical K?hler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound on Fano manifolds. This is based on our proofs of some openness theorems on the existence of twisted conical K?hler-Ricci solitons, which generalize Donaldson’s existence conjecture and the openness theorem of the conical K?hler-Einstein metrics to the conical soliton case. 相似文献
7.
We define a class of geometric flows on a complete Khler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equations, derivative nonlinear Schrdinger equations etc. Furthermore, we consider the existence for these flows from S~1into a complete Khler manifold and prove some local and global existence results. 相似文献
8.
Mihai PAUN Institut lie Cartan Université Henri Poincaré Nancy BP Vandoeuvre-lès-Nancy Cedex France. 《数学年刊B辑(英文版)》2008,(6)
The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact Khler manifolds. 相似文献
9.
We study conjugate points on a type of Khler manifolds, which are submanifolds of Grassmannian manifolds. And then we give the applications to the study of the index of geodesics and homotopy groups. 相似文献
10.
BingLong Chen 《中国科学 数学(英文版)》2012,55(5):893-912
In this paper,we prove a general existence theorem of Khler-Einstein metrics on complete Khler manifolds.We use the heat equation method smoothing certain positive (1,1) current in the canonical class. 相似文献
11.
12.
Boyong CHEN Yang LIU 《数学年刊B辑(英文版)》2008,(6)
The authors obtain a holomorphic Lefschetz fixed point formula for certain non-compact "hyperbolic" Khler manifolds (e.g. Khler hyperbolic manifolds, bounded domains of holomorphy) by using the Bergman kernel. This result generalizes the early work of Donnelly and Fefferman. 相似文献
13.
In this paper, the Hirota bilinear method is applied to a nonlinear equation which is a deformation to a KdV equation with a source. Using the Hirota’s bilinear operator, we obtain its bilinear form and construct its bilinear Bcklund transformation. And then we obtain the Lax representation for the equation from the bilinear Bcklund transformation and testify the Lax representation by the compatibility condition. 相似文献
14.
We discuss a class of complete Khler manifolds which are asymptotically complex hyperbolic near infinity . The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincaré inequality case and establish a vanishing theorem provided that the weighted function ρ is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighte... 相似文献
15.
《中国科学 数学(英文版)》2017,(4)
We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Khler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Khler S~3× S~3 is also obtained. Here, a Lagrangian submanifold is called J-isotropic, if there exists a function λ, such that g((▽h)(v, v, v), J v) = λ holds for all unit tangent vector v. 相似文献
16.
《数学年刊B辑(英文版)》2015,(1)
A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection.The vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds. 相似文献
17.
XiaoJiang Tan 《中国科学A辑(英文版)》2008,51(4):721-727
In this paper,we give some conditions on the surjective of multiply maps H~0(R,L)×H~0(R,K)→H~0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle. 相似文献
18.
The onset of melting in a class of simple metals is considered for an applied heat flux q_0=h_0/t~(1/2) at the boundary. Reduction of the nonlinear problem to a linear canonical form is obtained by a reciprocal transformation. Bounds are obtained on h_0 for melting to occur. 相似文献
19.
ChengJie Yu 《中国科学 数学(英文版)》2017,60(2):285-300
We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds. 相似文献
20.
LI Song-Ying & WEI DongHuan School of Mathematics Computer Science Fujian Normal University Fuzhou China 《中国科学 数学(英文版)》2010,(3)
The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these metrics u ( u h = 0) in B n , then h must be pluriharmonic in B n . In fact, it is a characterization theorem, as a consequence, the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails. The results in this paper generalize the theorems of Graham (1983) and examples constructed by Graham and Lee (1988). 相似文献