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
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