共查询到20条相似文献,搜索用时 296 毫秒
1.
研究局部对称空间中具有正Ricci曲率的完备极小子流形,得到了关于子流形Ricci曲率的一个pinching定理,把Norio Ejiri的结论从外围空间为球空间推广到局部对称空间中。 相似文献
2.
We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold with decomposable ? is a Calabi‐Eckmann manifold or the Riemannian product of a sphere and . We show that a complete, simply connected, normal metric contact pair manifold with decomposable ?, such that the foliation induced by the vertical subbundle is regular and reflections in the integral submanifolds of the vertical subbundle are isometries, is the product of globally ?‐symmetric spaces or the product of a globally ?‐symmetric space and . Moreover in the first case the manifold fibers over a locally symmetric space endowed with a symplectic pair. 相似文献
3.
本文对于局部对称黎曼流形中的伪脐点子流形给出了一个积分不等式,推广了Chen,B.Y.的一个相应的结果. 相似文献
4.
XuSenlin ChenDongmei 《分析论及其应用》2004,20(4):383-390
The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized 相似文献
5.
局部对称共形平坦黎曼流形中的紧致子流形 总被引:1,自引:0,他引:1
本文研究局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形的性质,通过一个代数不等式的证明,改进了已有的结果. 相似文献
6.
JIN Quanqin 《中国科学A辑(英文版)》2000,43(12):1279-1293
In this paper, we determine a large class of totally geodesic submanifolds of a compact Riemannian symmetric space. The stability
of these submanifolds in their ambient space is also determined. 相似文献
7.
8.
关于局部对称空间中的伪脐子流形 总被引:8,自引:0,他引:8
本文讨论了局部对称完备黎曼流形中的紧致伪脐子流形,且具有平行平均山率向量场。得到了这类子流形成为全脐子流形及其余维数减小的几个拼挤定理。 相似文献
9.
研究局部对称δ-拼挤黎曼流形中紧致的极小子流形,给出了若干个整体的拼挤定理,推广了S.S.Chern,M.do Carm o,S.K obayash i及S.T.Y au相应的结果. 相似文献
10.
本文研究局部对称共形平坦黎曼流形中紧致极小子流形,得到了这类子流形第二基本形式模长平方关于外围空间Ricci曲率的—个拼挤定理,推广了文[1]中的结果. 相似文献
11.
Given a compact symmetric space, M, we obtain the mean exit time function from a principal orbit, for a Brownian particle starting and moving in a generalized ball whose boundary is the principal orbit. We also obtain the mean exit time flmction of a tube of radius r around special totally geodesic submanifolds P of M. Finally we give a comparison result for the mean exit time function of tubes around submanifolds in Riemannian manifolds, using these totally geodesic submanifolds in compact symmetric spaces as a model. 相似文献
12.
局部对称共形平坦黎曼流形中的紧致子流形 总被引:6,自引:0,他引:6
本文讨论局部对称共形平坦黎曼流形中紧子流形问题.改进了[1]的结果并将[2]中关于球面子流形的一个结果推广到局部对称共形平坦黎曼流形子流形. 相似文献
13.
We prove a gap rigidity theorem for diagonal curves in maximal polyspheres of irreducible compact Hermitian symmetric spaces of tube type, which is a dual analog to a theorem obtained by Mok. Motivated by the proof we show that the Chow space of certain totally geodesic submanifolds is affine algebraic, which gives a weaker version of gap rigidity for a class of higher dimensional submanifolds. 相似文献
14.
Huafei Sun 《Geometriae Dedicata》2002,90(1):63-75
We study minimal submanifolds in the locally symmetric and conformally flat Riemannian manifold and generalize Yau's result obtained in J. Amer. Math. 97 (1975), 76–100. 相似文献
15.
Sebastian Klein 《Geometriae Dedicata》2009,138(1):25-50
The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature
tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from
its Satake diagram, in a way that is suited for the use with computer algebra systems; an example implementation for Maple Version 10 can be found on . As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
相似文献
16.
In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in aLocally symmetric and conformally flat Riemannian mainfold N~(+p).When N~(+p)is a space S_(1)~(+p) of constantcurvature,our theorems reduce to the theorems of[1],[2]. 相似文献
17.
Barbara Opozda 《Geometriae Dedicata》1998,69(1):1-14
We propose to study n-dimensional purely real submanifolds of the standard affine complex space Cn from an affine point of view. Such submanifolds are naturally endowed with a unique transversal bundle. Fundamental theorems are given as well as a theorem of Cartan–Norden type. Examples illustrating particular affine properties of such submanifolds are provided. 相似文献
18.
利用对称空间的对偶性,本文建立局部强凸对称等仿射球之集与某复空间形式中的极小对称Lagrange子流形之集间的对应关系,在自然定义的等价意义下,这是一一对应关系.作为这种对应关系的直接应用,本文用完全不同的方法重新证明胡泽军等人最近建立的一个重要定理.该定理对具有平行Fubini-Pick形式的局部强凸等仿射球进行了完全分类. 相似文献
19.
Curved flats,pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms 总被引:1,自引:0,他引:1
David Brander 《Annals of Global Analysis and Geometry》2007,32(3):253-275
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first
aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences
between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary,
we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second
aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and
that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case,
extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold.
We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.
相似文献
20.
Satoshi Ishikawa 《Journal of Functional Analysis》2003,204(1):50-100
We investigate the totally geodesic Radon transform which assigns a function to its integration over totally geodesic symmetric submanifolds in Riemannian symmetric spaces of noncompact type. Our main concern is focused on the injectivity and support theorem. Our approach is based on the projection slice theorem relating the totally geodesic Radon transform and the Fourier transforms on symmetric spaces. Our approach also uses the study of geometry concerned with the totally geodesic symmetric subvarieties in Riemannian symmetric spaces in terms of the cell structure of the Satake compactifications. 相似文献