Submanifolds with Prescribed Mean Curvature Vector.
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This paper is a survey of results on topological structures and curvature structures of complete submanifolds in a Euclidean space.
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We obtain a pointwise inequality valid for all submanifolds of all real space forms with and with codimension two, relating its main scalar invariants, namely, its scalar curvature from the intrinsic geometry of , and its squared mean curvature and its scalar normal curvature from the extrinsic geometry of in .
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