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Klingenberg, W.

Über kompakte Riemannsche Mannigfaltigkeiten. (German) Zbl 0133.15004

Math. Ann. 137, 351-361 (1959).
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Keywords:

Riemannian manifolds
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Full Text: DOI EuDML

References:

[1] Bonnet, O.: Sur quelques propriétés des lignes géodésiques. C. R. Acad. Sci. (Paris)40, 1311-1313 (1855).
[2] Cartan, E.: Leçons sur la géométrie des espaces de Riemann. 2e éd. Paris 1946. · Zbl 0060.38101
[3] Hadamard, J.: Les surfaces à courbures opposées, J. Math. pures appl. (5),4, 27-73 (1898). · JFM 29.0522.01
[4] Klingenberg, W.: On the structure of compact Riemannian manifolds. Proc. nat. Acad. Sci. (Wash.)44, 586-588 (1958). · Zbl 0135.40302 · doi:10.1073/pnas.44.6.586
[5] Klingenberg, W.: Contributions to Riemannian geometry in the large. Ann. of Math.69, No. 2 (1959). · Zbl 0133.15003
[6] Morse, M.: A generalization of the Sturm separation and comparison theorems inn-space. Math. Ann.103, 52-69 (1930). · JFM 56.1078.03 · doi:10.1007/BF01455690
[7] Mut?, Y.: Some properties of geodesics in the large in a twodimensional Riemannian manifold with positive curvature. Sci. Rep. Yokohama Nat. Univ. Sect. I2, 1-12 (1953).
[8] Myers, S. B.: Riemannian manifolds in the large. Duke math. J.1, 39-49 (1935). · Zbl 0011.22502 · doi:10.1215/S0012-7094-35-00105-3
[9] Myers, S. B.: Connections between differential geometrie and topology. Duke math.1, 376-391 (1935). · Zbl 0012.27502 · doi:10.1215/S0012-7094-35-00126-0
[10] Pogorelov, A.: A theorem regarding geodesics on closed convex surfaces. Math. Sb. N. S.18, 181-183 (60) (1946). · Zbl 0061.37612
[11] Rauch, H. E.: A contribution to differential geometry in the large, Ann. of Math.54, 38-55 (1951). · Zbl 0043.37202 · doi:10.2307/1969309
[12] Schoenberg, I. J.: Some applications of the calculus of variations to Riemannian geometry. Ann. of Math.33, 485-495 (1932). · Zbl 0005.29903 · doi:10.2307/1968530
[13] Whitehead, J. H. C.: On the covering of a complete space by the geodesics through a point. Ann. of Math.36, 679-704 (1935). · Zbl 0012.27802 · doi:10.2307/1968651
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