COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

VOLUME GROWTH ESTIMATES OF MANIFOLDS WITH NONNEGATIVE CURVATURE OUTSIDE A COMPACT SET

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.

THEOREMS OF BARTH-LEFSCHETZ TYPE ON KAHLER MANIFOLDS WITH PARTIALLY POSITIVE CURVATURE

The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partiallypositive bisectional curvature without the assumption of nonnegative bisectional curvature.Some applications of the results to holomorphic mappings are given.

The Chern-Ricci flow and holomorphic bisectional curvature

In this note, we show that on Hopf manifold S^(2n-1)×S^1, the non-negativity of the holomorphic bisectional curvature is not preserved along the Chern-Ricci flow.

Characterizations of Null Holomorphic Sectional Curvature of GCR-Lightlike Submanifolds of Indefinite Nearly Khler Manifolds

We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.

Parallel Translation on Kahler Manifolds

In this paper, the author establishs a real-valued function on K?hler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K?hler manifolds, then they are holomorphically isometric.

VANISHING THEOREMS FOR ACH KHLER MANIFOLDS AND HARMONIC MAPS

We discuss a class of complete Kaihler 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 Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.

ON A KHLER VERSION OF CHEEGER-GROMOLL-PERELMAN'S SOUL THEOREM

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.

完备正曲率凯拉流形的体积增长与曲率衰减

在C^n上构造了一族全纯截曲率为正的凯拉度量,并证明所构造的度量具有如下性质：当测地距离ρ趋于无穷时,测地球的体积增长为O(■),而黎曼标量曲率的衰减为O(■),其中β≥0．

Nonpositively Curved Almost Hermitian Metrics on Product of Compact Almost Complex Manifolds

In this paper, we give a classification of almost Hermitian metrics with nonpositive holo- morphic bisectional curvature on a product of compact almost complex manifolds. This generalizes previous results of Zheng [Ann. of Math. （2）, 137（3）, 671-673 （1993）] and the author [Proc. Amer. Math. Soc., 139（4）, 1469-1472 （2011）].

全纯截面曲率与Kahler-like度量

本文研究具有给定全纯截面曲率条件的Kahler-like流形.首先,证明具有非零常值全纯截面曲率的Kahler-like流形一定是Kahler流形;其次,证明关于Hermite曲率流的抛物Schwarz引理;最后,给出具有正全纯截面曲率的紧致Kahler-like流形上的消没定理.

复乘积流形上Berwald度量与强Khler-Finsler度量的构造(英文)

在一般的复乘积流形上构造了一类光滑的Finsler度量,证明了该度量是Berwald度量.得到了该度量的全纯曲率并在一定条件下证明了所构造的度量是强Kahler-Finsler度量.

实双截曲率为零的三维紧Hermite流形

复几何中的一个经典猜想是,任何全纯截曲率为常数的紧Hermite流形必为Kahler或Chern平坦的.该猜想在2维时已被证明.本文对该猜想在3维时的一个特殊情形给出证明:实双截曲率为0的紧3维Hermite流形必为Chern平坦的.实双截曲率是全纯截曲率概念的推广,由Yang和Zheng(2019)引入.该曲率量在Kahler时与全纯截曲率等价,在非Kahler时比后者稍强.