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Transactions of the American Mathematical Society

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Extensions of the Rauch comparison theorem to submanifolds


Author: F. W. Warner
Journal: Trans. Amer. Math. Soc. 122 (1966), 341-356
MSC: Primary 53.74
DOI: https://doi.org/10.1090/S0002-9947-1966-0200873-6
MathSciNet review: 0200873
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References [Enhancements On Off] (What's this?)

  • [1] W. Ambrose, The Cartan structural equations in classical Riemannian geometry, J. Indian. Math. Soc. 24 (1960), 23-76. MR 0123996 (23:A1317)
  • [2] M. Berger, An extension of Rauch's metric comparison theorem and some applications, Illinois J. Math. 6 (1962), 700-712. MR 0143159 (26:719)
  • [3] R. Bishop and R. Crittenden, Geometry of manifolds, Academic Press, New York, 1964. MR 0169148 (29:6401)
  • [4] R. Hermann, Focal points of closed submanifolds of Riemannian spaces, Nederl. Akad. Wetensch. Proc. Ser. A 66 (1963), 613-628. MR 0158333 (28:1558)
  • [5] H. Rauch, A contribution to differential geometry in the large, Ann. of Math. 54 (1951), 38-55. MR 0042765 (13:159b)
  • [6] -, Geodesics and curvature in differential geometry in the large, Yeshiva Univ, Press, New York, 1959.

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DOI: https://doi.org/10.1090/S0002-9947-1966-0200873-6
Article copyright: © Copyright 1966 American Mathematical Society

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