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
DOI:
https://doi.org/10.1090/S0002-9939-1972-0296855-7
MathSciNet review:
0296855
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Abstract | References | Similar Articles | Additional Information
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.
- 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
Keywords:
Riemannian,
tubular neighborhood,
area function,
differential inequality,
constant curvature,
Cartan calculus
Article copyright:
© Copyright 1972
American Mathematical Society
