On isometric immersions in Euclidean space of manifolds with non-negative sectional curvatures
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- by Philip Hartman
- Trans. Amer. Math. Soc. 115 (1965), 94-109
- DOI: https://doi.org/10.1090/S0002-9947-1965-0202094-9
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References
- C. Carathéodory, Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Teubner, Leipzig, 1935.
- 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
- Shiing-shen Chern and Richard K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79 (1957), 306–318. MR 84811, DOI 10.2307/2372684
- 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
- Barrett O’Neill, Isometric immersion of flat Riemannian manifolds in Euclidean space, Michigan Math. J. 9 (1962), 199–205. MR 152970
- Richard Sacksteder, On hypersurfaces with no negative sectional curvatures, Amer. J. Math. 82 (1960), 609–630. MR 116292, DOI 10.2307/2372973
Bibliographic Information
- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 115 (1965), 94-109
- MSC: Primary 53.74
- DOI: https://doi.org/10.1090/S0002-9947-1965-0202094-9
- MathSciNet review: 0202094