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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Curvature pinching for three-dimensional minimal submanifolds in a sphere
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by Yi Bing Shen PDF
Proc. Amer. Math. Soc. 115 (1992), 791-795 Request permission

Abstract:

In this paper, some pinching theorems for the Ricci curvature and the scalar curvature of three-dimensional compact minimal submanifolds in a sphere are given.
References
  • S. S. Chern, M. do Carmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 59–75. MR 0273546
  • Norio Ejiri, Compact minimal submanifolds of a sphere with positive Ricci curvature, J. Math. Soc. Japan 31 (1979), no. 2, 251–256. MR 527542, DOI 10.2969/jmsj/03120251
  • Katsuya Mashimo, Minimal immersions of $3$-dimensional sphere into spheres, Osaka J. Math. 21 (1984), no. 4, 721–732. MR 765352
  • Yi Bing Shen, On intrinsic rigidity for minimal submanifolds in a sphere, Sci. China Ser. A 32 (1989), no. 7, 769–781. MR 1057998
  • James Simons, Minimal varieties in riemannian manifolds, Ann. of Math. (2) 88 (1968), 62–105. MR 233295, DOI 10.2307/1970556
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 791-795
  • MSC: Primary 53C42; Secondary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1093604-2
  • MathSciNet review: 1093604