Geodesic
On geodesic curves on quotient manifold of nondegenerate affinor fields
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 52-60

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We consider the quotient manifold of the manifold of nondegenerate affinor fields on a compact manifold with respect to the action of the group of nowhere vanishing functions. This manifold is endowed with a structure of infinite-dimensional Lie group. On this Lie group, we construct an object of linear connection with respect to which all left-invariant vector fields are covariantly constant (the Cartan connection). We also find the geodesics of the Cartan connection.
Keywords: infinite-dimensional differentiable manifold, Lie algebra, linear connection, left-invariant vector field, one-parameter subgroups of the Lie group, geodesic.
Mots-clés : Lie group, Cartan connection 
@article{IVM_2018_8_a6,
     author = {E. M. Romanova},
     title = {On geodesic curves on quotient manifold of nondegenerate affinor fields},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--60},
     publisher = {mathdoc},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_8_a6/}
}
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E. M. Romanova. On geodesic curves on quotient manifold of nondegenerate affinor fields. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 52-60. http://geodesic.mathdoc.fr/item/IVM_2018_8_a6/