Geodesic
On geodesic curves on quotient manifold of nondegenerate affinor fields
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 52-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2018},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_8_a6/}
}
TY  - JOUR
AU  - E. M. Romanova
TI  - On geodesic curves on quotient manifold of nondegenerate affinor fields
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 52
EP  - 60
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_8_a6/
LA  - ru
ID  - IVM_2018_8_a6
ER  - 
%0 Journal Article
%A E. M. Romanova
%T On geodesic curves on quotient manifold of nondegenerate affinor fields
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 52-60
%N 8
%U http://geodesic.mathdoc.fr/item/IVM_2018_8_a6/
%G ru
%F IVM_2018_8_a6
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/

[1] Postnikov M. M., Rimanova geometriya. Semestr V, Faktorial, M., 1998

[2] Romanova E. M., “Mnogoobrazie nevyrozhdennykh affinornykh polei”, Izv. vuzov. Matem., 2008, no. 7, 39–45

[3] Romanova E. M., “Svyaznost Kartana i ee geodezicheskie na mnogoobrazii nevyrozhdennykh affinornykh polei”, Izv. vuzov. Matem., 2009, no. 5, 68–72

[4] Burbaki N., Differentsiruemye i analiticheskie mnogoobraziya. Svodka rezultatov, Mir, M., 1975 | MR

[5] Burbaki N., Gruppy i algebry Li, gl. III, Mir, M., 1976

[6] Postnikov M. M., Gruppy i algebry Li. Lektsii po geometrii. Semestr V, Nauka, M., 1982 | MR