Kaehler流形的Sasaki子流形

Kaehler流形是偶维微分流形,奇维微分流形中,与之媲美的是Sasaki流形。它是正规、切触度量流形。关于Sasaki流形,有判别定理(见[1]中P_(272)定理5.1) 定理A 殆切触度量流形M是Sasaki流形的充要条件为 (xφ)Y=g(X,Y)ξ-g(Y,ξ)X。 (1) 我们知道,Kaehler流形的Sasaki实超曲面是Sasaki流形,其维数也是奇数。Bejancu成功地对Kaehler流形的反全纯子流形引入Sasaki结构,定义了Sasaki反全纯子流形,其维     

Kaehler流形的全脐实超曲面

给出了Ｋａｅｈｌｅｒ流形的全脐实超曲面的一个分类定理。     

Finsler流形间调和映射的第2变分

给出了Finsler流形间非蜕化映射的能量泛函的第1和第2变分公式, 并利用变分公式得到了从Finsler流形到Riemann流形的非常值稳定调和映射的若干不存在性定理.     

P-Sasakian流形的外蕴球面(英)

本文讨论了P－Sasakian流形的外蕴球面，并给出了P－Sasakian流形的外蕴球面的一个分类定理．     

P—Sasakian流形的外蕴球面

本文讨论了Ｐ－Ｓａｓａｋｉａｎ流形的外蕴球面，并给出了Ｐ－Ｓａｓａｋｉａｎ流形的外蕴球面的一个分类定理。     

Stiefel流形上的梯度下降法

基于Stiefel流形上算法的几何框架,本文提出了Stiefel流形上的梯度下降法.理论上给出了算法收敛性定理.三个数值仿真算例表明算法是有效的,与其他方法相比具有更快的收敛速度.     

积分流形的分支条件及其应用

通过使用压缩原理, 获得了一个关于积分流形存在的分支定理,作为应用,给出了一个高维系统积分流形存在的充分性条件. 特别地,证明了在奇异性为余维2的4维自治系统中3维不变环面的存在性和唯一性.     

奇数维spin~c流形和S~1作用(英文)

本文研究了奇数维spin~c流形上的等边指标定理.用这些指标定理和一些复分析的讨论,得到了两个奇数维spin~c流形上的Atiyah-Hirzebruch类型消灭定理,结果推广了刘-王的消灭定理.     

时滞惯性流形及近似时滞惯性流形族

时滞惯性流形是对耗散系统惯性流形、近似惯性流形的最新发展,它基于对 大小涡分量间相互作用更细致的观察,即改变了惯性流形和近似惯性流形方法中大小 涡分量间相互作用为瞬时行为的隐含假定,而认为这种作用与系统的历史相关的．本 文结出了一类耗散系统时滞惯性流形的存在性证明,由于其存在性不需要“谱间隔条 件”保证,因而时滞惯性流形是广泛存在的．随后我们引出了一类离散的时滞惯性流 形,并在此基础上构造了一种近似时滞惯性流形族,分别给出了它们近似时滞惯性流 形的误差估计,结果显示这种新方法为构造稳定和高精度的算法提供了可能．     

关于L流形的一些讨论

本文以Leibniz流形为基础,引入了L流形的概念,讨论了L流形的可积性,以及李群G在L流形上的作用,并给出了相应的例子.     

两个非紧致齐性复解析流形

本文给出两个非紧致的齐性复解析流形．用它的齐性子流形构造出两个例外对称典型域的扩充空间，并由复流形上的运动群在超圆上的限制得到了两个例外对称典型域的仿射自同胚群，它们是闭的辛子群．     

Locally Lagrange-Symplectic Manifolds

The symplectic forms which have a compatible tangent structure locally look like the symplectic form of a nondegenerate Lagrangian function. For this reason, the corresponding manifold is said to be locally Lagrange-symplectic. In the paper, we give some elementary properties of these manifolds, and discuss their symplectic reduction.     

Hessian Comparison and Spectrum Lower Bound of Almost Hermitian Manifolds

The authors obtain a complex Hessian comparison for almost Hermitian manifolds, which generalizes the Laplacian comparison for almost Hermitian manifolds by Tossati, and a sharp spectrum lower bound for compact quasi Kähler manifolds and a sharp complex Hessian comparison on nearly Kähler manifolds that generalize previous results of Aubin, Li Wang and Tam-Yu.     

Approximate Inertial Manifolds to the Newton-Boussinesq Equations

Approximate inertial manifolds are related to the study of long time behaviour of dissipative partial differential equa tions. In this paper, we construct two approximate inertial manifolds for the two dimensional Newton-Boussinesq Equations. The orders of approximations of these manifolds to the global attractor are derived.     

Banach流形上映射度

本文讨论一种无限维流形上拓扑不变量，即具有可定向Ｆｒｅｄｈｏｌｍ结构的实Ｂａｎａｃｈ流形上　　Ｃｒ　　映射度．它是通常有限维流形上光滑映射度的一种自然推广．     

Complete Flat Affine and Lorentzian Manifolds

Following in the tradition of Hilbert's 18th problem of classifying crystallographic groups, we provide a survey of a series of results which have culminated in the study of flat Lorentz manifolds. In particular, Milnor asked whether all complete flat affine manifolds have virtually polycyclic fundamental groups. Margulis answered this question negatively by constructing complete flat Lorentz manifolds with free fundamental groups. In this paper, we follow the effort to classify and understand these interesting counterexamples to Milnor's question, and their generalizations.     

Cohomogeneity Two Actions on Flat Riemannian Manifolds

In this paper, we study flat Riemannian manifolds which have codimension two orbits, under the action of a closed and connected Lie group G of isometries. We assume that G has fixed points, then characterize M and orbits of M.     

Some Global Optimization Problems on Stiefel Manifolds

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-known assignment problem.     

Geometric Heat Comparison Criteria for Riemannian Manifolds

The main results of this paper are small-time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustrate them by examples. Mathematics subject classifications (2000): 58J35, 35K05     

Holomorphic Maps of Compact Generalized Hopf Manifolds

We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds.