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Zbl 1081.53017
Grebenyuk, Marina
Connections associated with linear distributions. (English)
[A] Mladenov, Iva\"ilo 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. 218-230 (2005). ISBN 954-84952-9-5/pbk

In the present paper differential geometry is applied to multidimensional affine spaces. The method used is based on the differential geometrical method developed by {\it 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.
[Iulia Hirică (Bucureşti)]

MSC 2000:: *53B05 Linear and affine connections

Keywords: three-component distribution; affine connexion; projective connexion

Citations: Zbl 0053.42802

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