Nonholonomic (n + 1)-webs |
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Authors: | M. I. Kabanova A. M. Shelekhov |
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Affiliation: | 1. Moscow State Pedagogical University, ul. Malaya Pirogovskaya 1, Bld. 1, Moscow, 119991, Russia 2. Tver State University, 33 ul. Zhelyabova 33, Tver, 170000, Russia
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Abstract: | We consider a nonholonomic (n + 1)-web NW on an n-dimensional manifold M, i.e., n + 1 codimension 1 distributions on M. We prove that a web NW on M is equivalent to a G-structure with structure group λE, the group of scalar matrices. We find the structure equations of a web NW and the integrability conditions of the distributions of a web NW. It is shown that on a manifold with nonholonomic (n + 1)-web an affine connection Γ arises naturally for which the distributions of the web are totally geodesic. We consider the case when the connection Γ has zero curvature and, in particular, when a web NW is defined by invariant distributions on a Lie group. In the case when all distributions of a web NW on a Lie group are integrable, we find the equations of this group in terms of local coordinates. |
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