Two applications of the technique of length-decreasing variations
HTML articles powered by AMS MathViewer
- by Nathaniel Grossman PDF
- Proc. Amer. Math. Soc. 18 (1967), 327-333 Request permission
References
- M. Berger, An extension of Rauch’s metric comparison theorem and some applications, Illinois J. Math. 6 (1962), 700–712. MR 143159
- Theodore Frankel, Manifolds with positive curvature, Pacific J. Math. 11 (1961), 165–174. MR 123272
- T. Frankel, On the fundamental group of a compact minimal submanifold, Ann. of Math. (2) 83 (1966), 68–73. MR 187183, DOI 10.2307/1970471
- 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 W. Klingenberg, Riemannsche Geometrie im Grossen (Lecture notes prepared by D. Gromoll and W. Meyer), Bonn, 1962.
- Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018
- 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
- J. L. Synge, On the neighborhood of a geodesic in Riemannian space, Duke Math. J. 1 (1935), no. 4, 527–537. MR 1545898, DOI 10.1215/S0012-7094-35-00140-5
- F. W. Warner, Extensions of the Rauch comparison theorem to submanifolds, Trans. Amer. Math. Soc. 122 (1966), 341–356. MR 200873, DOI 10.1090/S0002-9947-1966-0200873-6
- J. H. C. Whitehead, On the covering of a complete space by the geodesics through a point, Ann. of Math. (2) 36 (1935), no. 3, 679–704. MR 1503245, DOI 10.2307/1968651
Additional Information
- © Copyright 1967 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 18 (1967), 327-333
- MSC: Primary 53.72
- DOI: https://doi.org/10.1090/S0002-9939-1967-0210048-9
- MathSciNet review: 0210048