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Connections associated with linear distributions. (English) Zbl 1081.53017
Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 218-230 (2005).
In the present paper differential geometry is applied to multidimensional affine spaces. The method used is based on the differential geometrical method developed by G. F. Laptev [Tr. Mosk. Mat. Soc. Obshch. 2, 275–382 (1953; Zbl 0053.42802)]. The three-component distribution of affine spaces is considered and some connections are constructed, generalizing the theory of regular and vanishing hyper-zones, zones, hyper-zone distributions, surface of full and non full rank. The results obtained can be applied to the general theory of distributions in multi-dimensional spaces and to the theory of connections, which are associated with multi-component distributions.
MSC:
53B05Linear and affine connections