Submanifolds in a euclidean hypersphere
Abstract: Let be an oriented closed -dimensional submanifold of a euclidean (-space . Let and be the position vector field and the mean curvature vector field of in . Then is contained in a hypersphere of centered at when and only when either or .
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Keywords: Position vector, mean curvature normal, mean curvature, Laplacian, support function, submanifold in a hypersphere
Article copyright: © Copyright 1971 American Mathematical Society