局部对称黎曼流形中的极小子流形

In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized.     

Minimal and Maximal Semigroups Related to Causal Symmetric Spaces

Let G/H be an irreducible globally hyperbolic semisimple symmetric space, and let S ³ G be a subsemigroup containing H not isolated in S. We show that if S^o p 0 then there are H-invariant minimal and maximal cones Cmin ³ Cmax in the tangent space at the origin such that H exp Cmin ³ S ³ HZK(a)expCmax. A double coset decomposition of the group G in terms of Cartan subspaces and the group H is proved. We also discuss the case where G/H is of Cayley type.     

非紧对称空间中子流形焦点和形算子间的关系

首先详细地讨论了非紧Ｌｉｅ群的度量和Ｃａｒｔａｎ分解,然后由Ｌｉｅ群和对称空间的关系得到了非紧对称空间中的子流形焦点存在的充要条件,同时还给出了焦点重数的计算方法．     

共形空间中的正则子流形

共形空间Qn1有Lorentz群的作用,首先证明了Lorentz空间Rn1中的稳态曲面是关于共形体积泛函的临界曲面,其次对共形空间Qn1中的共形迷向子流形作出了分类.     

高维空间中数据的相似性度量

高维空间中数据之间的相似性度量是目前数据挖掘、信息处理与检索等领域所面临的一个重要问题.文章在总结分析了高维数据的特点以及现有的一些度量方法的基础上,提出了一种新的度量方式,该方法在对高维数据进行相似性度量之前,首先对原始数据空间进行网格划分.文章的最后对其有效性作了定量分析,实验证明,该方式是行之有效的.     

Minimal Homogeneous Submanifolds in Euclidean Spaces

We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex homogeneous submanifold of C ^N must be totally geodesic.     

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.     

On Weakly Symmetric Spaces

The object of the present paper is to study the semi-decomposibility of a weakly symmetric space introduced by Tamássy and Binh [1]. Also a weakly symmetric space admitting a concurrent or a recurrent vector field has been studied.     

Semisimple Symplectic Symmetric Spaces

A symplectic symmetric space is a connected affine symmetric manifold M endowed with a symplectic structure which is invariant under the geodesic symmetries. When the transvection group G⁰ of such a symmetric space M is semisimple, its action on (M,) is strongly Hamiltonian; a classical theorem due to Kostant implies that the moment map associated to this action realises a G⁰-equivariant symplectic covering of a coadjoint orbit O in the dual of the Lie algebra of G⁰. We show that this orbit itself admits a structure of symplectic symmetric space whose transvection algebra is . The main result of this paper is the classification of symmetric orbits for any semisimple Lie group. The classification is given in terms of root systems of transvection algebras and therefore provides, in a symplectic framework, a theorem analogous to the Borel–de Siebenthal theorem for Riemannian symmetric spaces. When its dimension is greater than 2, such a symmetric orbit is not regular and, in general, neither Hermitian nor pseudo-Hermitian.     

常曲率空间中伪脐2-调和子流形(英文)

The conjecture [1] asserts that any biharmonic submanifold in sphere has constant mean curvature. In this paper, we first prove that this conjecture is true for pseudo-umbilical biharmonic submanifolds M n in constant curvature spaces S n+p (c)(c > 0), generalizing the result in [1]. Secondly, some sufficient conditions for pseudo-umbilical proper biharmonic submanifolds M n to be totally umbilical ones are obtained.     

Maximal Total Length Of k Disjoint Cycles In Bipartite Graphs

Let k, s and n be three integers with sk2, n2k+1. Let G=(V ₁,V ₂;E) be a bipartite graph with |V ₁|=|V ₂|=n. If the minimum degree of G is at least s+1, then G contains k vertex-disjoint cycles covering at least min(2n,4s) vertices of G.     

局部对称流形的全脐子流形

In this paper we obtain some formulas for totally umbilical submanifolds in a locally symmetric manifold, and derive some local results on the submanifolds from these formulas.     

Subspaces of Maximal Operator Spaces

We explore subspaces of maximal operator spaces ( submaximal spaces) and give a new characterization of such spaces. We show that the set of n-dimensional submaximal spaces is closed in the topology of c.b. distance, but not compact. We also investigate subspaces of MAX(L ) and prove that any homogeneous Hilbertian subspace of MAX(L ₁) is completely isomorphic to R + C.     

局部对称黎曼流形中的紧致极小子流形的Ricci曲率

设N ^n+p是截面曲率K_N 满足1/2 <δ≤ K_N≤ 1 的n+p维局部对称完备的δ-Pinching黎曼流形. Mⁿ是N^n+p 的紧致极小子流形. 该文讨论了这类子流形关于Ricci曲率有关的Pinching定理.     

Isometries on Noncommutative Symmetric Spaces

Doklady Mathematics - Let $$\mathcal{M}$$ be an atomless semifinite von Neumann algebra equipped with a faithful normal semifinite trace τ (or else, an atomic von Neumann algebra with all...     

Polar Foliations of Symmetric Spaces

We prove that a polar foliation of codimension at least three in an irreducible compact symmetric space is hyperpolar, unless the symmetric space has rank one. For reducible symmetric spaces of compact type, we derive decomposition results for polar foliations.