1) 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全脐子流形的几个充分条件。
2) 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。
4) totally-Umbilical
全脐点子流形
5) F-R totally umbilical
F-R全脐子流形
6) totally quasi-umbilical submanifold
全拟脐子流形
1.
Let M be a totally quasi-umbilical submanifold immersed in a space form.
本文研究全拟脐子流形中稳定积分流的不存在性，证明了在一定几何条件下，这类流形中不存在稳定积分流，由此得到几个同调群的消没定理。
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}，
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参考词条