Geodesic
Connection on the group of diffeomorphisms as a bundle over the space of functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 82-84 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Jacobian determines a bundle with total space consisting of orientation-preserving diffeomorphisms of a (connected) manifold over the space of positive functions on this manifold (with integral equal to volume for a compact manifold). It is proved that, for the $n$-sphere with standard metric, there is a unique connection on this bundle that is invariant with respect to all isometries of the sphere, and a description of this connection is given.
Keywords: group of diffeomorphisms, manifold of constant curvature, connection. 
@article{FAA_2021_55_3_a6,
     author = {S. M. Gusein-Zade},
     title = {Connection on the group of diffeomorphisms as a bundle over the space of functions},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--84},
     year = {2021},
     volume = {55},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a6/}
}
TY  - JOUR
AU  - S. M. Gusein-Zade
TI  - Connection on the group of diffeomorphisms as a bundle over the space of functions
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2021
SP  - 82
EP  - 84
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a6/
LA  - ru
ID  - FAA_2021_55_3_a6
ER  - 
%0 Journal Article
%A S. M. Gusein-Zade
%T Connection on the group of diffeomorphisms as a bundle over the space of functions
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2021
%P 82-84
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a6/
%G ru
%F FAA_2021_55_3_a6
S. M. Gusein-Zade. Connection on the group of diffeomorphisms as a bundle over the space of functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 82-84. http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a6/

[1] V. I. Arnold, B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, no. 125, Springer-Verlag, New York, 1998 | DOI | MR | Zbl

[2] S. M. Gusein-Zade, V. S. Tikunov, “Chislennye metody sozdaniya anamorfirovannykh kartograficheskikh izobrazhenii”, Geodeziya i kartografiya, 1990, no. 1, 38–44

[3] S. M. Gusein-Zade, V. S. Tikunov, Anamorfozy: chto eto takoe?, Editorial URSS, M., 1999