Radii of immersed manifolds and nonexistence of immersions
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- by Tôru Ishihara PDF
- Proc. Amer. Math. Soc. 78 (1980), 276-279 Request permission
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
- Howard Jacobowitz, Isometric embedding of a compact Riemannian manifold into Euclidean space, Proc. Amer. Math. Soc. 40 (1973), 245–246. MR 375173, DOI 10.1090/S0002-9939-1973-0375173-3 S. Kobayashi and K. Nomizu, Foundations of differential geometry, Interscience Tracts in Pure and Math., no. 15, Interscience, New York, 1969.
- John Douglas Moore, An application of second variation to submanifold theory, Duke Math. J. 42 (1975), 191–193. MR 377776
- Tominosuke Otsuki, On the existence of solutions of a system of quadratic equations and its geometrical application, Proc. Japan Acad. 29 (1953), 99–100. MR 60281
Additional Information
- © 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