Shiohama, Katsuhiro Busemann functions and total curvature. (English) Zbl 0433.53050 Invent. Math. 53, 281-297 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 11 Documents MSC: 53C70 Direct methods (\(G\)-spaces of Busemann, etc.) 53C22 Geodesics in global differential geometry Keywords:noncompact Riemannian manifold; distance function; Busemann function; Gaussian curvature; total curvature Citations:Zbl 0112.370 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Bangert, V.: Riemannsche Mannigfaltigkeiten mit nicht konstanter konvexer Funktionen. Arch. Math.,31, 163-170 (1978) · Zbl 0372.53021 · doi:10.1007/BF01226433 [2] Busemann, H.: The geometry of geodesics, New York: Academic Press INC. 1955 · Zbl 0112.37002 [3] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. of Math.,96, 413-443 (1972) · Zbl 0246.53049 · doi:10.2307/1970819 [4] Cheeger, J., Ebin, D.: Comparison theorems in riemannan geometry. Amsterdam-Oxford-New York: North Holland Math. Library 9, 1975 · Zbl 0309.53035 [5] Cohn-Vossen, S.: Kürzeste Wege und Totalkrümmung auf Flächen, Comp. Math.,2, 69-133 (1935) · JFM 61.0789.01 [6] Cohn-Vossen, S.: Totalkrümmung und geodätische Linien auf einfachzusammehängenden offenen vollständigen Flächenstücken. Recueil Math. Moskau,43, 139-163 (1936) · Zbl 0014.27601 [7] Greene, R., Shiohama, K.: Convex functions on complete noncompact manifolds, Preprint at UCLA, 1978 · Zbl 0468.53033 [8] Greene, R., Wu, H.: C? convex functions and manifolds of positive curvature. Acta Math.,137, 209-245 (1976) · Zbl 0372.53019 · doi:10.1007/BF02392418 [9] Gromoll, D., Meyer, W.: On complete open manifolds of positive curvature. Ann. of Math.,90, 75-90 (1969) · Zbl 0191.19904 · doi:10.2307/1970682 [10] Maeda, M.: On the total curvature of noncompact Riemannian manifolds, Kodai Math. Sem. Rep.,26, 95-99 (1974) · Zbl 0302.53021 · doi:10.2996/kmj/1138846952 [11] Poor, W.: Some results on nonnegatively curved manifolds, J. Differential Geometry,9, 583-600 (1974) · Zbl 0292.53037 [12] Shiohama, K.: An extension of a theorem of Myers, J. Math. Soc. Japan,27, 561-569 (1975) · Zbl 0311.53053 · doi:10.2969/jmsj/02740561 [13] Toponogov, A.: Riemannian spaces having their curvature bounded below by a positive number, Amer. Math. Soc. Transl.,37, 291-336 (1964) · Zbl 0136.42904 [14] Toponogov, A., Riemannian spaces which contain straight lines, Amer. Math. Soc. Transl.37, 287-290 (1964) · Zbl 0138.42902 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.