Parallel transportation for Alexandrov space with curvature bounded below (Q1380482)

By generalizing the work of \textit{I. G. Nikolaev} [Sib. Math. J. 24, 106-119 (1983; Zbl 0539.53030)], a ``synthetic'' parallel transportation along geodesics in Alexandrov spaces with curvature bounded below is constructed and an analog of the second variation formula is obtained here. As applications, Synge's lemma [\textit{J. L. Synge}, Q. J. Math., Oxf. Ser. 7, 316-320 (1936; Zbl 0015.41601)] and Frankel's theorem [\textit{T. Frankel}, Pac. J. Math. 11, 165-174 (1961; Zbl 0107.39002)] are extended from Riemannian manifolds to Alexandrov spaces.