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Indexed by:期刊论文

Date of Publication:1999-03-01

Journal:TAIWANESE JOURNAL OF MATHEMATICS

Included Journals:SCIE、Scopus

Volume:3

Issue:1

Page Number:55-72

ISSN No.:1027-5487

Key Words:normalized mean curvature vector field; normalized scalar curvature

Abstract: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.