Surfaces without conjugate points
HTML articles powered by AMS MathViewer
- by L. W. Green PDF
- Trans. Amer. Math. Soc. 76 (1954), 529-546 Request permission
References
- Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946. MR 0017881
- Herbert Busemann, Metric Methods in Finsler Spaces and in the Foundations of Geometry, Annals of Mathematics Studies, No. 8, Princeton University Press, Princeton, N. J., 1942. MR 0007251
- Herbert Busemann, Spaces with non-positive curvature, Acta Math. 80 (1948), 259–310. MR 29531, DOI 10.1007/BF02393651
- Herbert Busemann, Angular measure and integral curvature, Canad. J. Math. 1 (1949), 279–296. MR 30808, DOI 10.4153/cjm-1949-024-7 E. Cartan Leçons sur la géométrie des espaces de Riemann, Paris, 1946.
- Stefan Cohn-Vossen, Kürzeste Wege und Totalkrümmung auf Flächen, Compositio Math. 2 (1935), 69–133 (German). MR 1556908 J. Hadamard Les surfaces à courbures opposées, J. Math. Pures Appl. (5) vol. 4 (1898) pp. 27-73. F. Hausdorff Mengenlehre, Leipzig, 1927.
- Gustav A. Hedlund, Two-dimensional manifolds and transitivity, Ann. of Math. (2) 37 (1936), no. 3, 534–542. MR 1503297, DOI 10.2307/1968476
- Gustav A. Hedlund, The dynamics of geodesic flows, Bull. Amer. Math. Soc. 45 (1939), no. 4, 241–260. MR 1563961, DOI 10.1090/S0002-9904-1939-06945-0
- Eberhard Hopf, Closed surfaces without conjugate points, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 47–51. MR 23591, DOI 10.1073/pnas.34.2.47
- Eberhard Hopf, Statistik der Lösungen geodätischer Probleme vom unstabilen Typus. II, Math. Ann. 117 (1940), 590–608 (German). MR 2722, DOI 10.1007/BF01450032
- 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 H. von Mangoldt Geodätische Linien auf positiv gekrümmten Flächen, J. Reine Angew. Math. vol. 91 (1881) pp. 23-53.
- Harold Marston Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 (1924), no. 1, 25–60. MR 1501263, DOI 10.1090/S0002-9947-1924-1501263-9
- Marston Morse and Gustav A. Hedlund, Manifolds without conjugate points, Trans. Amer. Math. Soc. 51 (1942), 362–386. MR 6479, DOI 10.1090/S0002-9947-1942-0006479-X
- Tauno Salenius, Über geodätische Linien in gewissen dreidimensionalen Mannigfaltigkeiten, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1948 (1948), no. 47, 52 (German). MR 26386 H. Seifert and W. Threlfall Variationsrechnung im Grossen, Berlin, 1938. —Lehrbuch der Topologie, Leipzig, 1934.
- Aurel Wintner, On the non-existence of conjugate points, Amer. J. Math. 73 (1951), 368–380. MR 42005, DOI 10.2307/2372182
Additional Information
- © Copyright 1954 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 76 (1954), 529-546
- MSC: Primary 53.0X
- DOI: https://doi.org/10.1090/S0002-9947-1954-0063097-3
- MathSciNet review: 0063097