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.

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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 
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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/

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