Geodesic
The dual geometry of the Cartan distribution
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 73-78

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The paper is devoted to the study of intrinsic geometry of a Cartan distribution $\mathcal M$ in projective space $\mathrm{P}_{2m}$. We essentially use the hyperband distribution $\mathcal H$ in $\mathrm P_{2m}$ associated with $\mathcal M$. Using the duality theory, we construct, in the 4th differential neighborhood, a series of normalizations of $\mathcal M$. We also consider dual affine connections $\overset{1}{\nabla}$ and $\overset{2}{\nabla}$ induced by the dual normalization of the Cartan distribution $\mathcal M$.
Mots-clés : Cartan distribution
Keywords: dual normalization, affine connection. 
@article{IVM_2008_7_a7,
     author = {N. A. Kuz'mina},
     title = {The dual geometry of the {Cartan} distribution},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--78},
     publisher = {mathdoc},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_7_a7/}
}
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N. A. Kuz'mina. The dual geometry of the Cartan distribution. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 73-78. http://geodesic.mathdoc.fr/item/IVM_2008_7_a7/