References
Busemann, H.: The geometry of geodesics. New York: Academic Press 1955
Busemann, H.: Recent synthetic differential geometry. Berlin-Heidelberg-New York: Springer 1970
Cheeger, J., Gromoll, D.: On the structure of complete maniforlds of nonnegative curvature. Ann. of Math. (2)96, 415–443 (1972)
Cohn-Vossen, S.: Kürzeste Wege und Totalkrümmung auf Flächen. Compositio Math.2, 63–133 (1935)
Eberlein, P., O'Neill, B.: Visibility manifolds. Pacific J. Math.46, 45–109 (1973)
Eschenburg, J.-H.: Horospheres and the stable part of the geodesic flow. Math. Z.153, 237–251 (1977)
Gromoll, D., Meyer, W.: On complete open manifolds of positive curvature. Ann. of Math. (2)90, 75–90 (1969)
Innami, N.: A classification of BusemannG-surfaces which possess convex functions. Acta Math. (to appear)
Lewis, G.M.: Cut loci of points at infinity. Pacific J. Math.43, 675–690 (1972)
Maeda, M.: On the existence of rays. Sci. Rep. Yokohama Nat. Univ. Sect. I26, 1–4 (1979)
Maeda, M.: Remarks on the distribution of rays. Preprint
Nasu, Y.: On asymptotic conjugate points. Tôhoku Math. J. Ser. 2,7, 157–165 (1955)
Nasu, Y.: On asymptotes in metric spaces with non-positive curvature. Tôhoku Math. J. Ser. 2,9, 68–95 (1957)
Nasu, Y.: On asymptotes in two-dimensional metric spaces. Tensor New Ser.7, 173–184 (1957)
Shiohama, K.: Busemann function and total curvature. Invent. Math.53, 281–297 (1979)
Shiohama, K.: A role of total curvature on complete non-compact Riemannian 2-manifolds. Preprint
Wu, H.: An elementary method in the study of nonnegative curvature. Acta Math.142, 57–78 (1979)
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Innami, N. Differentiability of Busemann functions and total excess. Math Z 180, 235–247 (1982). https://doi.org/10.1007/BF01318907
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DOI: https://doi.org/10.1007/BF01318907