查询词典 submanifold

Researches the submanifolds in nested space,for constant curvature Riemannian submanifold in quasi-constant curvature manifold and pseudo-umbilical submanifold with parallel mean curvature vector in constant curvature Riemannian submanifold,presents three sufficient conditions for this pseudo-umbilical submanifold to be total-umibilical submanifold,generalizes the result of JI Yongqiang.

对于拟常曲率流形中的常曲率黎曼子流形以及常曲率黎曼子流形中具有平行中曲率向量的紧致伪脐子流形，给出了这种伪脐子流形是全脐子流形的3个充分条件，推广了纪永强的相关结果。

Bernstein type theorem; Quaternion Euclidean space; minimal Lagrangian graphs; Twisted special Lagrangian submanifold; twisted normal bundle; Austere submanifolds; Real space form; Complex space form; Hamiltonian minimal submanifold; A Lagrangian submanifold with conformal Maslov form

基础科学，数学，几何、拓扑伯恩斯坦型定理；四元数欧氏空间；极小拉格朗日图；扭曲特殊拉格朗日子流形；扭曲法丛； Austere子流形；实空间形式；复空间形式；哈密尔顿极小子流形；具有共形Maslov形式的拉格朗日子流形

On the other hand, given calibration ξ in Rn+l, if it statisfies Frobenius condition, there is ξ-submanifold through every point. We know that each ξ- submanifold is homologically volume minimizing in Rn+1, so that every minimal hypersurface in Rn+1 is stable locally.

反之，给定R~(n+1)上的calibrationζ，如果它满足Frobenius可积条件，则过每一点有ζ的积分子流形M，我们知道ζ的积分子流形在其同调类中体积最小，自然M也局部是R~(n+1)中的稳定极小子流形。

We can costruct an exterior n-form ξ for every hypersurface M in Euclidean space Rn+1. The submanifold M is minimal if and only if is closed (dξ= 0), then ξ is calibration and M is ξ-submanifold.

我们证明了对于欧氏空间R~(n+1)中每一超曲面M，可以构造η-微分式ζ，而超曲面极小的条件恰是ζ为闭形式，即dζ=0的条件。

Three sufficient conditions are given for pseudo-umbilical submanifold to be a totally umbilical submanifold in constant space.

给出了这种伪脐子流形是全脐子流形的3个充分条件。

The data submanifold embedding into the field action model submanifold, which realizes the structure approximation; ii .

在信息几何的em学习算法的基础上，我们提出了对偶校正学习算法和基于拓扑结构逼近校正学习理论。

We still study a complete noncompact space-like submanifold ina pseudo-Euclidean space R_p~, and obtain some sufficient conditions for thespace-like submanifold to have finite many ends in this thesis.

本文还获得了伪欧氏空间R_p~中完备非紧的类空子流形具有有限个端的充分条件。

As face space is always believed to be a low-dimensional submanifold embedded in high-dimensional ambient space, many methods of subspace feature extraction adopt manifold learning to explore intrinsic structure of face patterns.

在人脸识别中，提取有效的鉴别特征是实现人脸准确识别的一个关键因素。

On the other hand, Let M~n be an z-dimensional complete noncompactoriented submanifold with finite total curvature in an-dimensional simplyconnected space form F~ of constant curvature c. In this thesis, we provethat if M satisfies one of the following: n≥3, c=0 and integral from n=M H~n＜∞;n≥5, c=-1 and H＜1-2/n~(1/2); n≥3, c=1 and H is bounded, where Hdenotes the mean curvature of M. then the dimension of the space of L~2 harmonic1-forms on M is finite.

本文还证明：若具常曲率c的完备单连通空间型F~中具有有限全曲率的n维完备非紧可定向子流形M满足下面条件之一：n≥3，c=0且integral from n=M H~n＜∞；n≥5，c=-1且H＜1-2/n~(1/2；n≥3，c=1且H有界的，则M上L~2调和1-形式空间的维数是有限的，这里H为M的平均曲率。

Submanifold; Homology group; Topological sphere theorem; L~2 harmonic 1-forms; Ends; Eigenvalue; Mean curvature; Second fundamental form

基础科学，数学，几何、拓扑子流形；同调群；拓扑球面定理； L~2调和1-形式；端；特征值；平均曲率；第二基本形式

I think people in this lifetime in a rebirth.

我觉得人在这一生里其实也在轮回。

He had to tie her hands together.

他不得不把她的双手绑在一起。