Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 222, Pages 134–140
DOI: https://doi.org/10.36535/0233-6723-2023-222-134-140 (Mi into1148) 		 
On Cartan's canonical projective connection

Yu. I. Shevchenkoa, E. V. Skrydlovaa, A. V. Vyalovab

a Immanuel Kant Baltic Federal University, Kaliningrad
b Kaliningrad State Technical University
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DOI: https://doi.org/10.36535/0233-6723-2023-222-134-140
Abstract: 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, torsion tensor, affine curvature-torsion tensor, canonical projective connection.
Document Type: Article
UDC: 514.76
MSC: 53B10
Language: Russian
Citation: Yu. I. Shevchenko, E. V. Skrydlova, A. V. Vyalova, “On Cartan's canonical projective connection”, 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, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 222, VINITI, Moscow, 2023, 134–140
Citation in format AMSBIB
\Bibitem{SheSkrVya23}
\by Yu.~I.~Shevchenko, E.~V.~Skrydlova, A.~V.~Vyalova
\paper On Cartan's canonical projective connection
\inbook 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
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 222
\pages 134--140
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1148}
\crossref{https://doi.org/10.36535/0233-6723-2023-222-134-140}
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