Geodesic
On Cartan's canonical projective connection
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 3, Tome 222 (2023), pp. 134-140

Voir la notice de l'article provenant de la source Math-Net.Ru

The projective Cartan connection is reduced to the canonical form using the deformation tensor, which is an extended torsion tensor. The curvature-torsion tensor of the canonical projective connection is degenerated into an analog of the centroprojective curvature tensor. The projective connection becomes canonical only when the extended torsion tensor vanishes.
Keywords: projective Cartan connection, curvature-torsion tensor, affine curvature-torsion tensor, canonical projective connection.
Mots-clés : torsion tensor 
@article{INTO_2023_222_a11,
     author = {Yu. I. Shevchenko and E. V. Skrydlova and A. V. Vyalova},
     title = {On {Cartan's} canonical projective connection},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {134--140},
     publisher = {mathdoc},
     volume = {222},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_222_a11/}
}
TY  - JOUR
AU  - Yu. I. Shevchenko
AU  - E. V. Skrydlova
AU  - A. V. Vyalova
TI  - On Cartan's canonical projective connection
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 134
EP  - 140
VL  - 222
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_222_a11/
LA  - ru
ID  - INTO_2023_222_a11
ER  - 
%0 Journal Article
%A Yu. I. Shevchenko
%A E. V. Skrydlova
%A A. V. Vyalova
%T On Cartan's canonical projective connection
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 134-140
%V 222
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_222_a11/
%G ru
%F INTO_2023_222_a11
Yu. I. Shevchenko; E. V. Skrydlova; A. V. Vyalova. On Cartan's canonical projective connection. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 3, Tome 222 (2023), pp. 134-140. http://geodesic.mathdoc.fr/item/INTO_2023_222_a11/