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Geodesic loops and some classes of affinely connected manifolds. (English) Zbl 0976.53501
Summary: The paper provides a survey of fundamental concepts, techniques and results of a new branch of mathematics which may be called “Odular Geometry” [see L. V. Sabinin, Sov. Math. Dokl. 18, No. 2, 515-518 (1977; Zbl 0375.53021), L. V. Sabinin and P. O. Mikheev, Quasigroups and Differential Geometry. In: “Quasigroups and Loops: Theory and Applications”, Sigma Ser. Pure Math. 8, 357-430 (1990; Zbl 0721.53018)]. Now these ideas and methods are widely recognized in the mathematical world and are very perspective, especially in applications to algebra, geometry and mathematical physics. The presentation is based on original works of professor L. V. Sabinin and his school. The list of references encounts 27 titles.
53C05 Connections (general theory)
53C80 Applications of global differential geometry to the sciences
53C22 Geodesics in global differential geometry