Extrinsic rigidity theorems for compact submanifolds of the sphere.
نویسندگان
چکیده
منابع مشابه
Rigidity of Compact Minimal Submanifolds in a Sphere
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. T...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1970
ISSN: 0022-040X
DOI: 10.4310/jdg/1214429644