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Proceedings of the American Mathematical Society

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On characterization of Riemannian manifolds by growth of tubular neighborhoods

Author: Nathaniel Grossman
Journal: Proc. Amer. Math. Soc. 32 (1972), 556-560
MSC: Primary 53C20
MathSciNet review: 0296855
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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 [Enhancements On Off] (What's this?)

  • 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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Keywords: Riemannian, tubular neighborhood, area function, differential inequality, constant curvature, Cartan calculus
Article copyright: © Copyright 1972 American Mathematical Society