查询词典 submanifold

The compact minimal submanifold of a Locally symmetric and conformally flat Riemannian manifold are studied, and obtain the following intrinsic rigidity theorem.

研究了局部对称共形平坦黎曼流形的紧致极小子流形，即设M是局部对称共形平坦黎曼流形的n维紧致极小子流形，得到了这种子流形的若干内蕴刚性积分不等式，给出了流形全测地的限制条

We consider Grassmann manifold G(2,8) as a submanifold of the unit sphere of /\2 which is the exterior vector space on Rn. Thus we have the induced metric and connection on G(2, n).

把Grassmann流形G（2，n）看作等距地嵌入在欧氏空间R~n上2-外向量空间∧~2中的单位球面上的子流形，得到它上面的度量和联络。

In [33] and [34], a nice generalization of minimal Lagrangian submanifolds called Hamiltonian-minimal submanifold was introduced and investigated by Y.G.

Oh在[33]和[34]中最先引进的哈密尔顿极小拉格朗日子流形，此类子流形式是对极小拉格朗日子流形一种很好的推广，同时他对此类子流形作了相应的研究。

The main results of the thesis are as follows: Theorem 1 M~is a locally symmetric Bochner-Kaehler manifold,Let M~n be a compact Kaehler submanifold with flat normal bundle in M~.

主要结果如下：定理1 M~是局部对称Bochner-Kaehler流形，设M~n是M~中法丛平坦的紧致Kaehler子流形。

Let M~n(n≥3)be an n-dimensional complete noncompact oriented submanifold in an-dimensional Euclidean space R~.

他们还进一步证明：若M具有有限指标，则M上L~2调和1-形式空间的维数是有限的，且M仅有有限个端[35]。

Keywords: harmonic map;pluriharmonic maps; submanifold

中文关键词：调和映照；多重调和映照；子流形

In this paper by use of a new differential operator similar as one introduced by Cheng and Yau,we obtain a rigidity result for a compact submanifold of constant scalar curvature in a unit sphere.

宣满友 ，盛为民本文利用一个类似于Cheng和Yau引进的微分算子的新微分算子，得到了单位球面中常数量率的紧致子流形的一个刚性结果。

It is also considered to study the Finsler geometry which deal with the Chern''s connection、flag curvature、Ricci scalar of Finsler manifolds、Finsler submanifold geometry, and harmonic maps between Finsler manifolds.

研究芬斯勒几何的某些问题，包括芬斯勒流形的陈省身联络、旗曲率、Ricci数量、芬斯勒子流形几何以及芬斯勒流形间的调和映射等。

Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.

定理4局部对称Bochner-Kaehler流形中不存在具有非零平行平均曲率向量且截面曲率大于零的紧致全实2-调和子流形。

Theorem 3 Let M~n be a compact totally real 2-harmonic submanifold in M~n which is a locally symmetric Bochner-Kaehler manifold.If Ricci curvature of M~n is nonegative and positive at a point at least,then the holomorphic sectional curvature of M~n is a postive constant number.

定理3设M~n是局部对称Bochner-Kaehler流形M~n的紧致全实2-调和子流形，若M~n的Ricci曲率非负且至少在一点为正，则M~n具有正常数全纯截面曲率。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。