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2004•Journal of Nanchang UniversityRequires access

ON SUBMANIFOLDS WITH CONSTANT MEAN CURVATURE

Qiu Tian-zhen

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Abstract

Let S~(n+p)(c) be an n+p dimensional Riemannian manifold of constant curvature c and M an n dimensional compact submanifold of S~(n+p)(c).It is known that there are Simons' and Yau's inequalities when M is minimal.In the present paper we give the generalizations of these inequalities for the case that the mean curvature vector field of M is parallel.-

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Let S~(n+p)(c) be an n+p dimensional Riemannian manifold of constant curvature c and M an n dimensional compact submanifold of S~(n+p)(c).It is known that there are Simons' and Yau's inequalities when M is minimal.In the present paper we give the generalizations of these inequalities for the case that the mean curvature vector field of M is parallel.-

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Available abstract

Let S~(n+p)(c) be an n+p dimensional Riemannian manifold of constant curvature c and M an n dimensional compact submanifold of S~(n+p)(c).It is known that there are Simons' and Yau's inequalities when M is minimal.In the present paper we give the generalizations of these inequalities for the case that the mean curvature vector field of M is parallel.-

Key concepts: Submanifold, Mathematics, Mean curvature, Constant (computer programming), Constant curvature, Riemannian manifold, Curvature, Vector field

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