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Proceedings of the American Mathematical Society

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On spherical submanifolds with nullity


Authors: Marcos Dajczer and Detlef Gromoll
Journal: Proc. Amer. Math. Soc. 93 (1985), 99-100
MSC: Primary 53C42; Secondary 53C40
DOI: https://doi.org/10.1090/S0002-9939-1985-0766536-0
MathSciNet review: 766536
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Abstract: We derive a new condition for spherical submanifolds with positive relative nullity. As an application we obtain that the Ricci curvature is bounded from above by the curvature of the ambient space.


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

  • [A] K. Abe, Some remarks on a class of submanifolds in space forms of non-negative curvature, Math. Ann. 247 (1980), 275-278. MR 568992 (82a:53056)
  • [F] D. Ferus, Isometric immersions of constant curvature manifolds, Math. Ann. 217 (1975), 155-156. MR 0407769 (53:11540)
  • [M] R. Miyaoka, Complete hypersurfaces in the space form with three principal curvatures, Math. Z. 179 (1982), 345-354. MR 649037 (83k:53076)
  • [O'N-S] B. O'Neill and E. Stiel, Isometric immersions of constant curvature manifolds, Michigan Math. J. 10 (1963), 335-339. MR 0158329 (28:1554)
  • [R] L. Rodriguez, Immersions of non-zero relative nullity in manifolds of constant positive curvature, Arch. Math. 32 (1979), 181-184. MR 534930 (80f:53035)

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DOI: https://doi.org/10.1090/S0002-9939-1985-0766536-0
Article copyright: © Copyright 1985 American Mathematical Society

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