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论文类型：期刊论文

发表时间：1999-03-01

发表刊物：TAIWANESE JOURNAL OF MATHEMATICS

收录刊物：SCIE、Scopus

卷号：3

期号：1

页面范围：55-72

ISSN号：1027-5487

关键字：normalized mean curvature vector field; normalized scalar curvature

摘要：Let M-n be a closed submanifold immersed into a real hyperbolic space form Hn+P of constant curvature -1. Denote by R the normalized scalar curvature of M-n and by H the mean curvature of M-n. Suppose that R is constant and bigger than or equal to -1. We first extend Cheng-Yau's technique to higher codimensional cases. Then, for Mn with parallel normalized mean curvature vector field, we show that, if H satisfies a certain inequality, then M-n is totally umbilical or the equality part holds. We describe all M-n whose H satisfies this equality.