两点齐性的 Finsler 流形

该文证明任何一个两点齐性的 Finsler 流形一定是黎曼流形. 证明过程中作者将泛函分析中经典的Mazur 定理推广到不一定是绝对齐次的 Minkowski 空间上.     

两点齐性的Finsler流形

该文证明任何一个两点齐性的Finsler流形一定是黎曼流形．证明过程中作者将泛函分析中经典的Mazur定理推广到不一定是绝对齐次的Minkowski空间上．     

复齐性有界域的全纯自同构群的显式

熟知最大连通全纯自同构群Aut(D)(0)是三角群T(D)和复齐性有界域D中一固定点的最大连通迷向子群Iso(D)(0)的半直乘积,而且任一复齐性有界域都全纯同构于正规Siegel域D(V_N,F)．本文给出T(D(V_N,F))和Iso(D(V_N,F))(0)中全纯自同构的明显表达式,其中G(0)是Lie群G的单位连通分支．     

对称空间和齐性等参子流形

本文讨论了对称空间和齐性等参子流形之间的密切关系,并利用Satake图（B,θ）给出对称空间G／K的迷向表示的主K-轨道与齐性等参子流形M之间的一一对应,同时还得到（B,θ）与标有重数的Dynkin图D（M）之间的对应     

非紧致复对称空间上平方函数算子的弱1-1有界性

利用复对称空间上热核的表达式,非紧致Riemann对称空间上热核的一个梯度估计及Stromberg的一个结果,证明了复对称空间上Littlewood-Paley平方函数算子的弱1-1有界性.     

非紧致复对称空间上平方函数算子的弱1-1有界性

利用复对称空间上热核的表达式,非紧致Ｒｉｅｍａｎｎ对称空间上热核的一个梯度估计及Ｓｔｒｏｍｂｅｒｇ的一个结果,证明了复对称空间上 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙ平方函数算子的弱 １－１有界性．     

四维洛伦兹空间中形状算子不可对角化且有两个不同主曲率类时共形齐性超曲面的分类

如果对任意两点p,q∈M₁³,都存在洛伦兹空间R₁⁴中的一个共形变换σ,使得σ(x(p))=x(q),并且σ(x(M₁³))=x(M₁³),则称x(M₁³)为共形齐性超曲面.在本文中我们主要研究形状算子不可对角化且具有2个不同主曲率的类时共形齐性超曲面x:M₁³→R₁⁴.通过定义共形不变度量g_c,典则提升Y,共形切标架{E_i}和典则法标架ξ,我们给出了这类超曲面的一个完备共形不变量系统{E₁,E₂,E₃}.接下来利用可积性条件构造出了这类超曲面的显式表达式及相应的共形变换子群,从而得到了对这类超曲面的分类定理.     

Banach空间中两个非扩张非自映象对公共不动点的逼近

设E是一致凸的Banach空间,C是E的非空有界闭凸子集而且是E的非扩张收缩核.设S,T:C→E是两个非扩张非自映象.本文证明了,在一定条件下,由(1.1)式定义的序列{xn}分别弱和强收敛于S,T的公共不动点.本文结果也推广和改进了最近一些人的最新结果.     

Integrability of Analytic Almost Complex Structures on Banach Manifolds

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic Banach manifolds. With this result at hand, we extend some known results concerning existence of invariant complex structures on homogeneous spaces of Banach–Lie groups. By way of illustration, we construct the complex flag manifolds associated with unital C^*-algebras.Mathematics Subject Classifications (2000): primary 32Q60; secondary 53C15, 58B12.     

Systems of Roots and Topology of Complex Flag Manifolds

In this paper we study the topology of a complex homogeneous space M = G/H of complex dimension n, with non vanishing Euler characteristic and G of type A, D, E by means of a topological invariant ₂, which is related to the Poincaré polynomial of M. We introduce the function Q = ₂/n and we examine how it varies as one passes from a principal orbit of the adjoint representation of a compact Lie group G to a more singular one. Moreover, it is proved that if M is a principal orbit G/T then Q depends only on the Weyl group of G.     

The Symmetry of 2-Flat Homogeneous Spaces

A Riemannian manifold M is called 2-flat homogeneous if every geodesic is contained in some 2-flat , and if the group of isometries of M acts transitively on the set of pairs (p, ) with p . By a 2-flat we mean a closed, connected, flat, totally geodesic, 2-dimensional submanifold of M. It is proved in the paper that 2-flat homogeneous spaces are symmetric.     

A Class of Homogeneous Einstein Manifolds

A Riemannian manifold (M, g) is called Einstein manifold if its Ricci tensor satisfies r = c·g for some constant c. General existence results are hard to obtain, e.g., it is as yet unknown whether every compact manifold admits an Einstein metric. A natural approach is to impose additional homogeneous assumptions. M. Y. Wang and W. Ziller have got some results on compact homogeneous space G/H. They investigate standard homogeneous metrics, the metric induced by Killing form on G/H, and get some classification results. In this paper some more general homogeneous metrics on some homogeneous space G/H are studies, and a necessary and sufficient condition for this metric to be Einstein is given. The authors also give some examples of Einstein manifolds with non-standard homogeneous metrics.     

On the Existence of Homogeneous Geodesics in Homogeneous Riemannian Manifolds

It is proved that every homogeneous Riemannian manifold admits a geodesic which is an orbit of a one-parameter group of isometries.     

Introduction to Actions of Discrete Groups on Pseudo-Riemannian Homogeneous Manifolds

Isometric actions of discrete groups are not always properly discontinuous for pseudo-Riemannian manifolds. This short exposition gives an up-to-date survey of some of the basic questions about discontinuous groups for pseudo-Riemannian homogeneous spaces, on which a rapid development has been made since late 1980s.The first half includes an elementary geometric motivation, the Calabi–Markus phenomenon, the discontinuous dual, and deformation. These topics are rebuilt on a criterion of properly discontinuous actions on homogeneous spaces of reductive groups, obtained by Kobayashi [Math. Ann. 1989] and generalized independently by Benoist [Ann. Math. 1996] and Kobayashi [J. Lie Theory 1996].The second half discusses the existence problem of compact Clifford–Klein forms of pseudo-Riemannian homogeneous spaces, for which many new methods from different areas have been recently employed. We examine these various approaches in some typical cases. We also point out that Zimmer's examples on SL(n)/SL(m) [J. Amer. Math. Soc. 1994] and Shalom's examples on SL(n)/SL(2) [Ann. Math. 2000] are readily obtained as special cases of Kobayashi's criterion [Duke Math. J. 1992], where the former uses ergodic theory and restrictions of unitary representations, respectively, while the latter uses cohomologies of discrete groups.The article also explains some open problems and conjectures.     

Some Remarks on Almost and Stable Almost Complex Manifolds

In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10-manifold M with H₁(M;?) = 0 and no 2-torsion in H₁(M;?) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4-manifold to be almost complex in terms of Betti numbers and the dimension of the ±-eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections.     

A Structure Theorem for Homogeneous Spaces

A partial generalization of Sophus Lie’s triangular form for solvable Lie algebras is presented. As application one is led to an iterated fibration for arbitrary homogeneous spaces. In the case of compact homogeneous spaces, one concludes easily that the Euler number is ≥0.