RIGIDITY RESULTS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE VECTOR IN THE DE SITTER SPACE
نویسندگان
چکیده
منابع مشابه
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ing from (2.6), we obtain that ∫ M ( H1Hr −Hr+1 〈N ,a〉dV = 0. (3.1) We know from Newton inequality [2] that Hr−1Hr+1 ≤ H2 r , where the equality implies that k1 = ··· = kn. Hence Hr−1 ( H1Hr −Hr+1 ≥Hr ( H1Hr−1−Hr ) . (3.2) It derives from Lemma 2.1 that 0≤H1/r r ≤H1/r−1 r−1 ≤ ··· ≤H1/2 2 ≤H1. (3.3) Thus we conclude that Hr−1 ( H1Hr −Hr+1 ≥Hr ( H1Hr1 −Hr ≥ 0, (3.4) and if r ≥ 2, the equalities h...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2006
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089505002818