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Geodesic loops and local triple systems in an affinely connected space. (English) Zbl 0409.53008

MSC:
53B05 Linear and affine connections
22E10 General properties and structure of complex Lie groups
53C22 Geodesics in global differential geometry
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[1] M. Kikkawa, ?On local loops in affine manifolds,? J. Sci. Hiroshima Univ. A-I. Math.,28, 199-207 (1964). · Zbl 0141.19603
[2] L. V. Sabinin, ?The geometry of loops,? Theses of Lectures at the Fifth All-Union Conference on Contemporary Problems in Geometry, Samarkand (1972), p. 192.
[3] M. A. Akivis, Local Differentiable Quasigroups and Three-Webs of Multidimensional Surfaces. Study in the Theory of Quasigroups and Loops [in Russian], Shtiintsa, Kishinev (1973), pp. 3-12.
[4] M. A. Akivis, ?Local algebras of multidimensional three-webs,? Sib. Mat. Zh.,17, No. 1, 5-11 (1976).
[5] K. Yamaguti, ?On algebras of totally geodesic spaces (Lie triple systems),? J. Sci. Hiroshima Univ. A-I. Math.,21, 107-113 (1957). · Zbl 0084.18405
[6] E. Cartan, ?La geometrie des groupes de transformations,? J. Math. Pures Appl.,9, No. 6, 1-119 (1927). · JFM 53.0388.01
[7] E. Cartan, Geometry of Riemann Spaces [Russian translation], ONTI, Moscow-Leningrad (1936).
[8] M. A. Akivis, ?Three-webs of multidimensional surfaces,? Proceedings of the Geometrical Seminar of VINITI, Vol. 2, Moscow, Izd. Akad. Nauk SSSR (1969), pp. 7-31.
[9] P. I. Kovalev, ?Triple Lie systems and affinely connected spaces,? Mat. Zametki,14, No. 1, 107-112 (1973).
[10] N. Jacobson, Lie Algebras, Wiley (1962).
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