Curvature of closed hypersurfaces and non-existence of closed minimal hypersurfaces
HTML articles powered by AMS MathViewer
- by S. B. Myers PDF
- Trans. Amer. Math. Soc. 71 (1951), 211-217 Request permission
References
-
E. Cartan, Leçons sur la géométrie des espaces de Riemann, Paris, 1928.
L. P. Eisenhart, Riemannian geometry, Princeton, 1926.
- H. Hopf and W. Rinow, Ueber den Begriff der vollständigen differentialgeometrischen Fläche, Comment. Math. Helv. 3 (1931), no. 1, 209–225 (German). MR 1509435, DOI 10.1007/BF01601813
- Sumner Byron Myers, Riemannian manifolds in the large, Duke Math. J. 1 (1935), no. 1, 39–49. MR 1545863, DOI 10.1215/S0012-7094-35-00105-3
- Sumner Byron Myers, Connections between differential geometry and topology. I. Simply connected surfaces, Duke Math. J. 1 (1935), no. 3, 376–391. MR 1545884, DOI 10.1215/S0012-7094-35-00126-0
- 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 H. Hopf, Zum Clifford-Kleinschen Raumproblem, Math. Ann. vol. 95 (1925).
Additional Information
- © Copyright 1951 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 71 (1951), 211-217
- MSC: Primary 53.0X
- DOI: https://doi.org/10.1090/S0002-9947-1951-0044884-1
- MathSciNet review: 0044884