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@inproceedings{Deshmukh2000RigidityOC, title={Rigidity of Compact Minimal Submanifolds in a Sphere}, author={Sharief Deshmukh}, year={2000} }

- Published 2000

In this paper we study n-dimensional compact minimal submanifolds in S with scalar curvature S satisfying the pinching condition S > n(n − 2). We show that for p ≤ 2 these submanifolds are totally geodesic (cf. Theorem 3.2 and Corollary 3.1). However, for codimension p ≥ 2, we prove the result under an additional restrictions on the curvature tensor corresponding to the normal connection (cf. Theorem 3.1 and Corollary 4.1). We also show that the scalar curvature S of a non-totally geodesic n… CONTINUE READING