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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On closed minimal submanifolds in pinched Riemannian manifolds
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by Hong Wei Xu PDF
Trans. Amer. Math. Soc. 347 (1995), 1743-1751 Request permission

Abstract:

In this paper, we first prove a generalized Simons integral inequality for closed minimal submanifolds in a Riemannian manifold. Second, we prove a pinching theorem for closed minimal submanifolds in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by S. S. Chern, M. do Carmo, and S. Kobayashi and A. M. Li and J. M. Li respectively. Finally, we obtain a distribution theorem for the square norm of the second fundamental form of $M$ under the assumption that $M$ is a minimal submanifold with parallel second fundamental form in a Riemannian manifold.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1743-1751
  • MSC: Primary 53C42; Secondary 53C20, 53C40
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1243175-X
  • MathSciNet review: 1243175