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:

53B05 | Linear and affine connections |