局部对称共形平坦黎曼流形中紧致极小子流形的一个刚性定理

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.     

局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形

本文把[1]的结论推广到了环绕空间是局部对称共形平坦的情形,即获得了:设M~是局部对称共形平坦黎曼流形N~+p(p>1)中具有平行平均曲率向量的紧致子流形,如果则M~位于N~+p的全测地子流形N~+1中。其中S,H分别是M~的第二基本形式长度的平方和M~的平均曲率,T_C、t_c分别是N~+p的Ricci曲率的上、下确界,K是N~+p的数量曲率。     

关于局部对称共形平坦空间中具有常数量曲率的子流形

该文研究了局部对称共形平坦空间中具有常数量曲率的紧致子流形,证明了这类子流形的某些内蕴刚性定理.     

球空间S^n＋p（C）中的紧致极小子流形

设 M~n 是常曲率空间 S~(n+p)(c)的紧致极小子流形,设 K 和 Q 分别是 M~n 上每点各方向截面曲率和 Ricci 曲率的下确界,R 是 M~n 的数量曲率,本文利用 M~n 的内在量 KQ和 R,给出球空间中紧致极小子流形是全测地子流形的六个充分条件。     

关于复射影空间的三维全实极小子流形

本文给出复射影空间中三维紧致全实极小子流形的Ricci曲率和数量曲率的鞭些拼挤定理.特别是证得:若M³是CP³的紧致全实极小子流形且它的Ricci曲率大于1/6,则M³是全测地的.     

欧氏空间中闭子流形的拓扑

本文通过建立浸入在欧氏空间或欧氏球面中某些子流形的Ricci曲率的下界估计和同调群的消失定理,确定了这些子流形的拓扑特征。     

欧氏空间中闭子流形的拓扑

本文通过建立浸入在欧氏空间或欧氏球面中某些子流形的 Ricci 曲率的下界估计和同调群的消失定理,确定了这些子流形的拓扑特征.     

局部对称Bochner-Kaehler流形的Kaehler子流形(Ⅱ)

一、引言在[7]中,我们证明了下面的定理A 设M~(n p)是复n p维局部对称Bochner-Kaehler流形,M~n是M~(n p)的复n≥2维紧致Kaehler子流形。令其中Ric(M)_x表示M~(n p)在点x的Ricci曲率。若M~n的截曲率K_M满足     

四元数射影空间的全实伪脐子流形

本文给出了四元数射影空间中紧致全实伪脐子流形关于截面曲率和Ricci曲率的Pinching定理，并推广和改进了四元数射影空间中紧致全实极小流形的一些结果．     

复射影空间中具有平行平均曲率向量的一般子流形

本文研究了复射影空间中具有平行平均曲率向量的一般子流形曲率性质与几何性质之间的关系. 利用活动标架法, 获得了关于截面曲率, Ricci 曲率和第二基本形式模长的刚性定理, 推广和完善了相关文献的若干结果.     

对称等仿射球和极小对称Lagrange子流形的对应

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.     

Locally minimal topological groups 1

The aim of this paper is to go deeper into the study of local minimality and its connection to some naturally related properties. A Hausdorff topological group (G,τ) is called locally minimal if there exists a neighborhood U of 0 in τ such that U fails to be a neighborhood of zero in any Hausdorff group topology on G which is strictly coarser than τ. Examples of locally minimal groups are all subgroups of Banach-Lie groups, all locally compact groups and all minimal groups. Motivated by the fact that locally compact NSS groups are Lie groups, we study the connection between local minimality and the NSS property, establishing that under certain conditions, locally minimal NSS groups are metrizable. A symmetric subset of an abelian group containing zero is said to be a GTG set if it generates a group topology in an analogous way as convex and symmetric subsets are unit balls for pseudonorms on a vector space. We consider topological groups which have a neighborhood basis at zero consisting of GTG sets. Examples of these locally GTG groups are: locally pseudoconvex spaces, groups uniformly free from small subgroups (UFSS groups) and locally compact abelian groups. The precise relation between these classes of groups is obtained: a topological abelian group is UFSS if and only if it is locally minimal, locally GTG and NSS. We develop a universal construction of GTG sets in arbitrary non-discrete metric abelian groups, that generates a strictly finer non-discrete UFSS topology and we characterize the metrizable abelian groups admitting a strictly finer non-discrete UFSS group topology. Unlike the minimal topologies, the locally minimal ones are always available on “large” groups. To support this line, we prove that a bounded abelian group G admits a non-discrete locally minimal and locally GTG group topology iff |G|?c.     

Four-Dimensional Osserman Symmetric Spaces

It is shown that locally symmetric four-dimensional Osserman spaces are flat, locally isometric to a rank-one symmetric space or locally isometric to certain rank-two symmetric spaces.     

Locally symmetric complex affine hypersurfaces

In this paper we study non-degenerate locally symmetric complex affine hypersurfaces Mⁿ of the complex affine space, i.e. hypersurfaces satisfying R=0, where is the affine connection induced on Mⁿ by the complex affine structure on the complex affine space, and R is the curvature tensor of . We classify the non-degenerate locally symmetric hypersurfaces Mⁿ, n > 2, and the minimal non-degenerate locally symmetric hypersurfaces Mⁿ, n > 1.Aspirant N.F.W.O. (Belgium)     

Locally symmetric Finsler spaces in negative curvature

É. Cartan introduced in 1926 the Riemannian locally symmetric spaces, as the spaces whose curvature tensor is parallel. They also owe their name to the fact that, for each point, the geodesic reflexion is a local isometry. The aim of this Note is to announce a strong rigidity result for Finsler spaces. Namely, we show that a negatively curved locally symmetric (in the first sense above) Finsler space is isometric to a Riemann locally symmetric space.     

Local Intersection Cohomology of Baily�CBorel Compactifications

The local intersection cohomology of a point in the Baily–Borel compactification (of a Hermitian locally symmetric space) is shown to be canonically isomorphic to the weighted cohomology of a certain linear locally symmetric space (an arithmetic quotient of the associated self-adjoint homogeneous cone). Explicit computations are given for the symplectic group in four variables.     

The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank

In this paper we show that the geodesic flow on a compact locally symmetric space of nonpositive curvature has a unique invariant measure of maximal entropy. As an application to dynamics we show that closed geodesics are uniformly distributed with respect to this measure. Furthermore, we prove that the volume entropy is minimized at a compact locally symmetric space of nonpositive curvature among all conformally equivalent metrics with the same total volume.     

Locally Symmetric Contact Metric Manifolds

We show that a locally symmetric contact metric space is either Sasakian and of constant curvature 1 or locally isometric to the unit tangent sphere bundle (with its standard contact metric structure) of a Euclidean space.     

Locally Desarguesian spaces

In Riemannian spaces, locally Desarguesian spaces have constant curvature and are therefore locally symmetric. This does not hold for Finsler spaces, so that locally Desarguesian spaces represent a generalization other than the obvious one we studied previously of (certain) Riemannian symmetric spaces. In this paper we discuss them in detail; as an example of the results obtained we mention that a simply connected locally Desarguesian space without conjugate points is globally Desarguesian. Applications are then given to spaces which are locally symmetric in a wider sense. We also study (and in Minkowski spaces determine exactly) the properties of functions which measure the distance of a point from those on a line.     

Locally Symmetric Contact Metric Manifolds

We show that a locally symmetric contact metric space is either Sasakian and of constant curvature 1 or locally isometric to the unit tangent sphere bundle (with its standard contact metric structure) of a Euclidean space. The second author is corresponding author