湖北大学学报（自然科学版）
湖北大學學報（自然科學版）
호북대학학보（자연과학판）
2009年
4期
339-342
,共4页
常曲率黎曼流形%平行中曲率向量%伪脐子流形%全脐子流形
常麯率黎曼流形%平行中麯率嚮量%偽臍子流形%全臍子流形
상곡솔려만류형%평행중곡솔향량%위제자류형%전제자류형
Riemannian manifold%mean curvature vector%pseudo-umbilical sub-manifold%totally umbilical submanifold
研究常曲率黎曼流形N~(n+p)(c)中具有平行中曲率向量的紧致伪脐子流形M~n,得到子流形M~n的内在量K,Q,σ若满足一定关系可使M~n是全脐子流形.推广了徐仙发和纪永强的有关结果.
研究常麯率黎曼流形N~(n+p)(c)中具有平行中麯率嚮量的緊緻偽臍子流形M~n,得到子流形M~n的內在量K,Q,σ若滿足一定關繫可使M~n是全臍子流形.推廣瞭徐仙髮和紀永彊的有關結果.
연구상곡솔려만류형N~(n+p)(c)중구유평행중곡솔향량적긴치위제자류형M~n,득도자류형M~n적내재량K,Q,σ약만족일정관계가사M~n시전제자류형.추엄료서선발화기영강적유관결과.
Considered the compact pseudo-umbilical submanifold M~n with parallel mean curvatue vector in the Riemannian manifold N~(n+p) (c) with constant curvature c, and concluded that if the inherent quantities of M~n ,K,Q,σ, satisfied two suitable conditions then M~n must be a totally umbilical submanifold of N~(n+p) (c). The paper generalized the results which obtained by Xu Xian-fa and Ji Yong-qiang.
