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Methods of non-associative algebra in differential geometry. (English) Zbl 0945.20038
Kolář, Ivan (ed.) et al., Differential geometry and applications. Proceedings of the 7th international conference, DGA 98, and satellite conference of ICM in Berlin, Brno, Czech Republic, August 10-14, 1998. Brno: Masaryk University. 419-427 (1999).
This paper is a survey of a new vision of differential geometry which is based on the work of the author’s school during the last twenty six years.
The first part contains the foundations from a geometric point of view with emphasis on the smooth quasigroup theory. The notions of a geodesic odule, geoodular structure, canonical affine connection, flat space are defined. In the second part the author discusses the construction of loop action theory and promises for it applications to the different geometric matters.
For the entire collection see [Zbl 0923.00021].

MSC:
20N05 Loops, quasigroups
53C35 Differential geometry of symmetric spaces
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