On characterization of Riemannian manifolds by growth of tubular neighborhoods
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 0305315 (46:4445)
- H. Wu, A characteristic property of the euclidean plane, Michigan Math. J. 16 (1969), 141-148. MR 39 #7544. MR 0246240 (39:7544)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20
Retrieve articles in all journals with MSC: 53C20
Keywords: Riemannian, tubular neighborhood, area function, differential inequality, constant curvature, Cartan calculus
Article copyright: © Copyright 1972 American Mathematical Society