Affiliation:
1. Xianyang Normal University, School of Mathematics and Information Science, Xianyang, P.R. China
Abstract
Let Nn+p q(c) be an (n+p)-dimensional connected indefinite space form
of index q(1 ? q ? p) and of constant curvature c. Denote by ? : M ?
Nn+p q (c) the n-dimensional spacelike submanifold in Nn+p q (c),
? : M ? Nn+p q(c) is called a Willmore spacelike submanifold in
Nn+p q(c) if it is a critical submanifold to the Willmore functional
W(?) = ?q M ?n dv =?M (S-nH2)n/2 dv, where S and H
denote the norm square of the second fundamental form and the mean curvature
of M and ?2 = S ? nH2. If q = p, in [14], we proved some integral
inequalities of Simons? type and rigidity theorems for n-dimensional
Willmore spacelike submanifolds in a Lorentzian space form Nn+p q(c).
In this paper, we continue to study this topic and prove some integral
inequalities of Simons? type and rigidity theorems for n-dimensional
Willmore spacelike submanifolds in an indefinite space form Nn+p q(c)
(1 ? q ? p).
Publisher
National Library of Serbia
Cited by
1 articles.
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