Submanifolds of positive Ricci curvature in a Euclidean space |
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Authors: | Sharief Deshmukh |
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Institution: | (1) Department of Mathematics, College of Science, King Saud University, P.O. Box#2455, Riyadh, 11451, Saudi Arabia |
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Abstract: | In this paper we study the role of constant vector fields on a Euclidean space R
n+p
in shaping the geometry of its compact submanifolds. For an n-dimensional compact submanifold M of the Euclidean space R
n+p
with mean curvature vector field H and a constant vector field on R
n+p
, the smooth function is used to obtain a characterization of sphere among compact submanifolds of positive Ricci curvature (cf. main Theorem).
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Keywords: | Submanifolds in a Euclidean space Ricci curvature Mean curvature vector field |
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