Curvature of closed hypersurfaces and non-existence of closed minimal hypersurfaces
Author:
S. B. Myers
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
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References | Similar Articles | Additional Information
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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 https://doi.org/10.1007/BF01601813
- Sumner Byron Myers, Riemannian manifolds in the large, Duke Math. J. 1 (1935), no. 1, 39–49. MR 1545863, DOI https://doi.org/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 https://doi.org/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 https://doi.org/10.2307/1968651 H. Hopf, Zum Clifford-Kleinschen Raumproblem, Math. Ann. vol. 95 (1925).
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© Copyright 1951
American Mathematical Society