On the isometric immersions in Euclidean space of manifolds with nonnegative sectional curvatures. II
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- by Philip Hartman
- Trans. Amer. Math. Soc. 147 (1970), 529-540
- DOI: https://doi.org/10.1090/S0002-9947-1970-0262981-4
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References
- M. Berger, An extension of Rauch’s metric comparison theorem and some applications, Illinois J. Math. 6 (1962), 700–712. MR 143159
- Eugenio Calabi and Philip Hartman, On the smoothness of isometries, Duke Math. J. 37 (1970), 741–750. MR 283727
- Shiing-shen Chern and Nicolaas H. Kuiper, Some theorems on the isometric imbedding of compact Riemann manifolds in euclidean space, Ann. of Math. (2) 56 (1952), 422–430. MR 50962, DOI 10.2307/1969650
- D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Mathematics, No. 55, Springer-Verlag, Berlin-New York, 1968 (German). MR 0229177
- Philip Hartman, On exterior derivatives and solutions of ordinary differential equations, Trans. Amer. Math. Soc. 91 (1959), 277–293. MR 109236, DOI 10.1090/S0002-9947-1959-0109236-1
- Philip Hartman, On isometric immersions in Euclidean space of manifolds with non-negative sectional curvatures, Trans. Amer. Math. Soc. 115 (1965), 94–109. MR 202094, DOI 10.1090/S0002-9947-1965-0202094-9
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- Philip Hartman and Louis Nirenberg, On spherical image maps whose Jacobians do not change sign, Amer. J. Math. 81 (1959), 901–920. MR 126812, DOI 10.2307/2372995 R. Kulkarni, Curvature and metric, Thesis, Harvard University, Cambridge, Mass., 1967.
- Barrett O’Neill, Isometric immersion of flat Riemannian manifolds in Euclidean space, Michigan Math. J. 9 (1962), 199–205. MR 152970
- 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
- Richard Sacksteder, On hypersurfaces with no negative sectional curvatures, Amer. J. Math. 82 (1960), 609–630. MR 116292, DOI 10.2307/2372973
- Edsel Stiel, Isometric immersions of manifolds of nonnegative constant sectional curvature, Pacific J. Math. 15 (1965), 1415–1419. MR 188948
- V. A. Toponogov, On convexity of Riemannian spaces of positive curvature, Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), 674–676 (Russian). MR 0091503
- V. A. Toponogov, Riemannian spaces containing straight lines, Dokl. Akad. Nauk SSSR 127 (1959), 977–979 (Russian). MR 0108808
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 147 (1970), 529-540
- MSC: Primary 53.74
- DOI: https://doi.org/10.1090/S0002-9947-1970-0262981-4
- MathSciNet review: 0262981