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|Title:||On the curvature of minimal submanifolds in a sphere||Authors:||Leung, P.-F.||Keywords:||Mathematics Subject Classification (1991): 53C25||Issue Date:||Jun-1995||Citation:||Leung, P.-F. (1995-06). On the curvature of minimal submanifolds in a sphere. Geometriae Dedicata 56 (1) : 5-6. ScholarBank@NUS Repository. https://doi.org/10.1007/BF01263609||Abstract:||S. T. Yau proved in Amer. J. Math.97 (1975), p. 95, Theorem 15 that if the sectional curvature of an n-dimensional compact minimal submanifold in the (n + p)-dimensional unit sphere is everywhere greater than (p - 1)/(2 p - 1), then this minimal submanifold is totally geodesic. In this note we improve this bound for the case p ≥ 2 to (3 p - 2)/(6 p). © 1995 Kluwer Academic Publishers.||Source Title:||Geometriae Dedicata||URI:||http://scholarbank.nus.edu.sg/handle/10635/103782||ISSN:||00465755||DOI:||10.1007/BF01263609|
|Appears in Collections:||Staff Publications|
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