Complete space-like submanifolds in locally symmetric semi-definite spaces
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The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.
Key wordsspace-like submanifolds constant mean curvature flat normal bundle second fundamental form locally symmetric semi-definite space
AMS(2000)subject classification53C20 53C40
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