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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Radii of immersed manifolds and nonexistence of immersions

Author: Tôru Ishihara
Journal: Proc. Amer. Math. Soc. 78 (1980), 276-279
MSC: Primary 53C42; Secondary 83C99
MathSciNet review: 550512
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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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Keywords: Nonexistence of isometric immersions, radius, diameter, the second variation
Article copyright: © Copyright 1980 American Mathematical Society