References
W. Ballmann, M. Gromov, and V. Shroeder, “Manifolds of nonpositive curvature,” in: Progress in Mathematics,61, Birkhauser, 1985.
M. Gromov, “Hyperbolic manifolds, groups and actions,” Ann. of Math. Stud., Princeton,97, 183–215 (1981).
V. B. Marenich, “Horofunctions, Busemann functions, and ideal boundaries of open manifolds of nonnegative curvature,” Sibirsk. Mat. Zh.,34, No. 5, 103–119 (1993).
J. Cheeger and D. Gromoll, “On the structure of complete open manifolds of nonnegative curvature,” Ann. of Math.,96, No. 3, 413–443 (1972).
V. B. Marenich, The Holonomy Operator in Open Manifolds of Nonnegative Curvature [Preprint] [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk (1990).
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The research was supported by the Russian Foundation for Fundamental Research (grant 93-011-179).
Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 2, pp. 407–409, March–April, 1994.
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Marenich, V.B. On connection of the geometry of a four-dimensional open manifold with the topology of its ideal boundaries. Sib Math J 35, 367–368 (1994). https://doi.org/10.1007/BF02104783
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DOI: https://doi.org/10.1007/BF02104783