Extensions of the Rauch comparison theorem to submanifolds
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- by F. W. Warner
- Trans. Amer. Math. Soc. 122 (1966), 341-356
- DOI: https://doi.org/10.1090/S0002-9947-1966-0200873-6
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References
- W. Ambrose, The Cartan structural equations in classical Riemannian geometry, J. Indian Math. Soc. (N.S.) 24 (1960), 23–76 (1961). MR 123996
- M. Berger, An extension of Rauch’s metric comparison theorem and some applications, Illinois J. Math. 6 (1962), 700–712. MR 143159, DOI 10.1215/ijm/1255632714
- Richard L. Bishop and Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. MR 0169148
- Robert Hermann, Focal points of closed submanifolds of Riemannian spaces, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math. 25 (1963), 613–628. MR 0158333, DOI 10.1016/S1385-7258(63)50061-4
- H. E. Rauch, A contribution to differential geometry in the large, Ann. of Math. (2) 54 (1951), 38–55. MR 42765, DOI 10.2307/1969309 —, Geodesics and curvature in differential geometry in the large, Yeshiva Univ, Press, New York, 1959.
Bibliographic Information
- © Copyright 1966 American Mathematical Society
- 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