Submanifolds with parallel mean curvature vector in spheres

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概要

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• Let M<SUP>n</SUP> be a compact submanifold of a sphere with parallel mean curvature vector h. We introduce a tensor φ, related to h and the second fundamental form, and show that if φ satisfies a certain inequality, then φ≡0 and M<SUP>n</SUP> is totally umbilic or equality holds. The estimate is sharp in the sense that we describe all M<SUP>n</SUP> that satisfy this equality.

• 東北大学の論文

著者

• Santos Walcy

  Universidade Federal Do Rio De Janeiro

関連論文

• Submanifolds with parallel mean curvature vector in spheres

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