Abstract:Let M be a compact Riemannian manifold isometrically immersed in a complete Riemannian manifold N. By the radius of M in N, we mean the minimum of radii of closed geodesic balls in N which contain M. Using the concept of a radius, we will give a theorem about the nonexistence of isometric immersions, which is a generalization of J. D. Moore’s result.
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- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 276-279
- MSC: Primary 53C42; Secondary 83C99
- DOI: https://doi.org/10.1090/S0002-9939-1980-0550512-2
- MathSciNet review: 550512