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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0550512-2
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.


References [Enhancements On Off] (What's this?)

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  • [4] T. Otsuki, On the existence of solutions of a system of quadratic equations and its geometrical application, Proc. Japan Acad. 29 (1953), 99-100. MR 0060281 (15:647e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0550512-2
Keywords: Nonexistence of isometric immersions, radius, diameter, the second variation
Article copyright: © Copyright 1980 American Mathematical Society

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