On differential-geometric structures on a manifold of nonholonomic (<Emphasis Type="Italic">n</Emphasis> + 1)-web |
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Authors: | M I Kabanova |
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Institution: | 1.Moscow Pedagogical State University,Moscow,Russia |
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Abstract: | We consider a nonholonomic (n + 1)-web NW on an n-dimensional manifold M, i.e., n + 1 distributions of codimension 1. We prove that there exists an invariant pencil of projective connections on M. To an ordered nonholonomic (n + 1)-web on M, there corresponds a unique curvilinear (n + 1)-web on M and vice versa. This correspondence is defined by the polarity with respect to a certain invariant multilinear n-form or the barycentric subdivision of some (n - 1)- dimensional simplex. In conclusion, we consider, as a special case, a nonholonomic (n + 1)-web ANW of hyperplanes in the affine space. A web ANW generates an invariant pencil of affine connections. We also study the case when these connections are projective. |
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