1) holomorphic submanifold
全纯子流形
1.
Furthermore, we get the condition that its submanifold is holomorphic submanifold and space - like submanifold under the condition that peripheral manifold is indefinite complex space form.
首先考虑外围空间是复空间型的情形,得到了子流形是平坦流形或CR—乘积的条件,进一步考虑外围流形为更一般的不定复空间型,得到了它的子流形是全纯子流形和类空全纯子流形的条件。
2) anti-holomorphic submanifold
反全纯子流形
1.
In this paper, we give some characteristics for Sasakian anti-holomorphic submanifolds of a locally conformal Kaehler manifold, and prove that, for a Sasakian anti-holomorphic submanifold M of locally conformal Kaehler manifold , if M is orthogonal to Lee vector field B_0, then M is D-umbilical.
给出了局部共形Kaehler流形的Sasakian反全纯子流形的一些几何刻画 。
3) Sasakian anti-holomorphic submanifold
Sasakian反全纯子流形
1.
In this paper, we give some characteristics for Sasakian anti-holomorphic submanifolds of a locally conformal Kaehler manifold, and prove that, for a Sasakian anti-holomorphic submanifold M of locally conformal Kaehler manifold , if M is orthogonal to Lee vector field B_0, then M is D-umbilical.
给出了局部共形Kaehler流形的Sasakian反全纯子流形的一些几何刻画 。
4) totally umbilical submanifolds
全脐子流形
1.
In this paper, some properties of totally real and totally umbilical submanifolds of a complex projective space are obtained.
获得了复射影空间中全实全脐子流形的若干性质,并且证明了复射影空间中具有平行平均曲率向量的正曲率紧致全实子流形必是伪脐的。
2.
Some pinching theorems about totally real pseudo-umbilical submanifolds with parallel mean curvature vector becoming totallyreal and totally umbilical submanifolds are obtained by choosing a suitableframe ?eld.
通过选取合适的活动标架，获得具有平行平均曲率向量的全实伪脐子流形成为全实全脐子流形的若干Pinching定理。
5) Totally real submanifolds
全实子流形
1.
We deduce the Riemannian metric on complex projective space from Riemannian submersion π:S2n+1→CPn,get its volume element We also prove that one type totally real submanifolds of CPn is none but ndimensional sphere Sn.
用黎曼淹没π：Ｓ２ｎ＋１→ＣＰｎ诱导出ＣＰｎ上的黎曼度量及其在不同坐标系下的表达形式；算出其体积元，并得到ＣＰｎ上一类ｎ维全实子流形与ｎ维球面Ｓｎ等
2.
This dissertatian is mainly concernd with several problems of Kaehler submanifolds and totally real submanifolds in complex projective space.
本文分两章研究了复射影空间CP~(n+p)中Kaehler子流形和全实子流形的若干问题。
6) totally umbilical submanifold
全脐子流形
1.
A totally umbilical submanifold of constant curvature space;
常曲率空间中的全脐子流形
2.
For constant submanifolds in quasi-constant curvature Riemannian manifold,and pseudo-umbilical submanifold with parallel mean curvature vector in constant space,three sufficient conditions are given for pseudo-umbilical submanifold to be a totally umbilical submanifold in constant space.
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的具有平行平均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。
3.
Let M2n+p+q1 be a (n+p+q)-dimensional δ-Pinching Riemannian manifold,M1n+p(c1) be a (n+p)-dimensional with constant curvature c1 in M2n+p+q,let M "be a compact pseudo-umbilical submanifold with parallel mean curvature vector in Mn+p(c1),we give some sufficient conditions that M "be a totally umbilical submanifold in M1n+p(c1).
设M2n+p+q是其截面曲率KM2ABAB满足O<δ
补充资料：全测地流形
全测地流形
totally - geodesic manifold
全测地流形[tot叨y一ge映sicm田创ud;。。助。e reo八e-3“，ec肋e MH0r006p幻Ile]，全测地子流形(to七山y-罗团es ic subl几In面kl) Rle~空间(Ri~~nsPace)v“中的一个子流形M”，使得M”中的测地线(geodesic ljl犯)也是VN中的测地线.全测地子流形M’‘是用如下的特征来刻画的:对M”的每个法向量，其相应的第二基本形式(second fundametal form)为零;这等价于M”的所有法曲率为零.M.n.Bo如以oBcK浦撰【补注】一般Riem以11们流形中全测地子流形的存在是例外情形.反之，许多这种全测地子流形的存在在近期的各种研究中被用来刻画某些特殊流形，例如对称空问.见【Al}，
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条