Geodesic
A.\,D.~Alexandrov's problem for non-positively curved spaces in the sense of Busemann
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 10-35

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This paper is the last of a series devoted to the solution of Alexandrov's problem for non-positively curved spaces. Here we study non-positively curved spaces in the sense of Busemann. We prove that isometries of a geodesically complete connected at infinity proper Busemann space $X$ are characterizied as follows: if a bijection $f\colon X\to X$ and its inverse $f^{-1}$ preserve distance 1, then $f$ is an isometry.
Keywords: Alexandrov's problem, non-positive curvature, geodesic, isometry, $r$-sequence, geodesic boundary, horofunction boundary. 
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     author = {P. D. Andreev},
     title = {A.\,D.~Alexandrov's problem for non-positively curved spaces in the sense of {Busemann}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {10--35},
     publisher = {mathdoc},
     number = {9},
     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2010_9_a1/}
}
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P. D. Andreev. A.\,D.~Alexandrov's problem for non-positively curved spaces in the sense of Busemann. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 10-35. http://geodesic.mathdoc.fr/item/IVM_2010_9_a1/