四元空间形式中具有常数Kähler角的浸入曲面

对四元K(a)hler流形中的浸入曲面引入了K(a)hler角的概念,同时讨论K(a)hler角是常数的情形.主要结果是若xM→N(c)是具有常数Q-截面曲率c的实四维四元空间形式N(c)中具有常数K(a)hler角θ(sinθ≠0)的等距浸入曲面,则必有c=0.     

四元空间形式中具有常数Khler角的浸入曲面

对四元Khler流形中的浸入曲面引入了Khler角的概念,同时讨论Khler角是常数的情形.主要结果是:若x:M→N(c)是具有常数Q-截面曲率c的实四维四元空间形式N(c)中具有常数Khler角θ(sinθ≠0)的等距浸入曲面,则必有c=0.     

β-辛临界曲面上K(a)hler角的上界估计

对于K(a)hler曲面(M,g)上的β-辛临界曲面∑,如果存在q＞3使得Lq(∑)有界,那么我们对∑上的K(a)hler角给出一个上界估计,该估计只依赖于M,q,β和∑的Lq泛函.当q＞4时,这个估计是已知的,我们的结果推广了q的范围.     

K(a)hler流形上的Lagrange力学

讨论了K(a)hler流形上的Lagrange力学,并给出Lagrange算子、Lagrange方程、作用泛函、Hamilton原理和Hamilton方程等复的数学形式.     

K(a)hler流形上的不变形式和积分不变量

用现代微分几何理论和高等微积分把Poincare和Cartan-Poincare积分不变量的晕要思想和结果以及E．Cartan在经典力学中首先建立的积分不变量和不变形式的关系推广到Kahler流形上的Hamilton力学中去，得到相应的更广泛的结果．     

K(a)hler流形上的Hamilton力学

利用力学原理、现在微分几何理论和高等微积分把Hamilton力学推广至K(a)hler流形上,建立K(a)hler流形上Hamilton力学,并得到Hamilton向量场、Hamilton方程等复的数学形式.     

关于S~6中具有常数Khler角的非超极小浸入的一个唯一性定理(英文)

对于 Ｓ~６中具有常数Ｋａｈｌｅｒ角的非超极小浸入 ｘ：Ｒ~２→Ｓ~６,本文证明了一个定理,它揭示了其ＫＡａｈｅｒ角取值的孤立现象．     

强K(a)hler-Finsler流形上(p,q)形式的中值Laplace算子

本文给出了强K(a)hler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等.与K(a)hler流形上利用逆变基本张量[11]及其在Finsler流形上的变形[5,10]作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强K(a)hler-Finsler流形上的逆变密切Kahler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强K(a)hler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广.     

全纯截面曲率与K(a)hler-like度量

本文研究具有给定全纯截面曲率条件的K(a)hler-like流形.首先,证明具有非零常值全纯截面曲率的K(a)hler-like流形一定是K(a)hler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K(a)hler-like流形上的消没定理.     

S6中具有常数K(a)hler角和常数曲率的极小曲面

本文给出了近Ｋａｈｌｅｒ球面Ｓ６中具有常数Ｋａｈｌｅｒ角和常数曲率的极小曲面的例子,同时证明了两个唯一性定理．     

Hyper-Hermitian Quaternionic Kähler Manifolds

We call a quaternionic Kähler manifold with nonzero scalar curvature, whosequaternionic structure is trivialized by a hypercomplex structure, ahyper-Hermitian quaternionic Kähler manifold. We prove that every locallysymmetric hyper-Hermitian quaternionic Kähler manifold is locally isometricto the quaternionic projective space or to the quaternionic hyperbolic space.We describe locally the hyper-Hermitian quaternionic Kähler manifolds withclosed Lee form and show that the only complete simply connected suchmanifold is the quaternionic hyperbolic space.     

关于S^6中具有常数Kahler角的非超极小浸入的一个唯一性定理

对于Ｓ＾６中具有常数Ｋａｈｌｅｒ角的非超极小浸入ｘ：Ｒ＾２→Ｓ＾６,本文证明了一个定理,它揭示了其Ｋａｈｌｅｒ角取值的孤立现象。     

K(a)hler Finsler Metrics Are Actually Strongly K(a)hler

In this paper,the K(a)hler conditions of the Chern-Finsler connection in complex Finsler geometry are studied,and it is proved that K(a)hler Finsler metrics are actually strongly K(a)hler.     

S~6中具有常数Kahler角的极小曲面

球面Ｓ６具有典型的近复结构，因而对于其中的曲面可引入Ｋａｈｌｅｒ角的概念．本文研究Ｓ６内具有常数Ｋａｈｌｅｒ角的极小曲面，得到了刚性定理．结合已有结果，易知Ｓｉｍｏｎ猜想对于这类曲面成立．     

A Theorem on Infinitesimal I-isometry of Surfaces Immersed in a Space with Constant Curvature

1.IntroductionTheproblemsofinfinitesimalrigidityandisometricdeformationhavebeenextensivelyin-vestigatedforsurfacesinthreedimensionalEuclideanspaceE'.See,forexample,A.SvecL1]'E.Kann[2j,ZhouJiazu[3Jandthepapers[4j,[5J,[6JbyYangWenmao3also,KobayashiandNomizu[7].ThefirstauthorandZhangGaoyonggeneralizedthetheoryofinfinitesimali-sometriesofsurfacesinE3tothehypersurfacesimmersedinaspaceofconstantcurvature[8j.K.Tenenblat[9]andR.A.GoldsteinandP.J.Ryan[1o]studiedtheinfinitesimalI-isometryfors…     

Compact Kähler Surfaces with Trivial Canonical Bundle

The classical conjectures of Weil on K3 surfaces – that the set of suchsurfaces is connected; that a version of the Torelli theorem holds; thateach such surface is Kähler; and that the period map issurjective – are reconsidered in the light of a generalisation of theNakai–Moishezon criterion, and short proofs of all the conjectures aregiven. Most of the proofs apply equally or with minor variation tocomplex 2-tori, the only other compact Kähler surfaces with trivialcanonical bundle.     

Complete Minimal Kähler Surfaces in R6

We construct the first examples of minimal Kähler surfaces in R⁶ which are irreducible and neither holomorphic nor complex ruled.     

Kähler Surfaces of Positive Scalar Curvature

We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface.