Submanifolds associated with graphs

In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.

     

k-order Slant Toeplitz Operators on the Bergman Space

In this paper κ-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed.     

飞秒光参量放大中三波群速失配的补偿

为了消除群速失配对参量放大的不利影响，描述了利用脉冲波面倾斜与非共线相位匹配相结 合，完全补偿飞秒光参量放大（OPA）中三波群速失配的新方法.计算了在BBOⅠ类、Ⅱ类相 位匹配条件下， 三波实现群速匹配时，相位匹配角、脉冲波面倾斜角以及非共线角随信号 光波长的变化.并分析了三波群速匹配对空间走离长度、参量增益和参量带宽的影响.结果表 明，在BBOⅠ类、Ⅱ类相位匹配条件下，利用该方法均能实现飞秒OPA连续调谐时三波的群速 匹配，从而大大增加了三波的有效互作用长度，为能够获得高增益，窄脉宽的参量光脉冲提 供了理论依据和指导. 关键词： 群速匹配 脉冲波面倾斜 非共线相位匹配 飞秒光参量放大     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．     

SLANT SUBMANIFOLDS OF A RIEMANNIAN PRODUCT MANIFOLD

In this article, the geometry of the slant submanifolds of a Riemannian product manifold is studied. Some necessary and sufficient conditions on slant, bi-slant and semi-slant submanifolds are given. We research fundamental properties of the distributions which are involved in definitions of semi- and bi-slant submanifolds in a Riemannian product manifold.     

$\delta$-拼挤流形中的2-调和子流形

We study biharmonic submanifolds in δ-pinched Riemannian manifolds, and obtain some sufficient conditions for biharmonic submanifolds to be minimal ones.     

Three classes of smooth Banach submanifolds in B(E,F)

Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. ＜ ∞ or codim R(T) = const.＜ ∞} and {T ∈ R(E, F) RankT =const.＜∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry.     

Diophantine vectors in analytic submanifolds of Euclidean spaces

Let M be an m-dimensional analytic manifold in R~n.In this paper,we prove that almost all vectors in M (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vector in M.     

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.