Geodesic
On differential-geometric structures on a~manifold of nonholonomic $(n+1)$-web
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 3-9

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We consider nonholonomic $(n+1)$-web $NW$ consisting of $n+1$ distributions of codimension $1$ on $n$-dimensional manifold $M$. We prove that an invariant pencil of projective connections exists on the manifold $M$. A unique curvilinear $(n+1)$-web corresponds to the ordered nonholonomic $(n+1)$-web and vice versa. The correspondence is defined by the polarity with respect to an invariant multilinear $n$-form or barycentric subdivision of an $(n+1)$-dimensional simplex. In conclusion we consider nonholonomic $(n+1)$-webs in affine space. The invariant pencil of affine connections is generated by every affine web. We also consider the case when the connections of the pencil are projective.
Keywords: nonholonomic $(n+1)$-web, curvilinear $(n+1)$-web, affine connection, affine nonholonomic $(n+1)$-web, projective connections, geodesic line. 
@article{IVM_2015_7_a0,
     author = {M. I. Kabanova},
     title = {On differential-geometric structures on a~manifold of nonholonomic $(n+1)$-web},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_7_a0/}
}
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M. I. Kabanova. On differential-geometric structures on a~manifold of nonholonomic $(n+1)$-web. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2015_7_a0/