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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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On characterization of Riemannian manifolds by growth of tubular neighborhoods
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by Nathaniel Grossman PDF
Proc. Amer. Math. Soc. 32 (1972), 556-560 Request permission

Abstract:

If the area function of the tubular neighborhoods of a compact submanifold of a Riemannian manifold satisfies a certain linear differential inequality, then the codimension of the submanifold is at most the order of that inequality.
References
  • R. A. Holzsager and H. Wu, A characterization of two-dimensional Riemannian manifolds of constant curvature, Michigan Math. J. 17 (1970), 297–299. MR 305315
  • H. Wu, A characteristic property of the euclidean plane, Michigan Math. J. 16 (1969), 141–148. MR 246240
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 32 (1972), 556-560
  • MSC: Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0296855-7
  • MathSciNet review: 0296855