Geodesic
Geometry of cyclic and anticyclic spaces
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. 10-18.

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We consider spaces whose geometry is determined by forms that are not quadratic. These forms are related to cyclic and anticyclic linear algebras. We describe linear transformations that preserve these forms and indicate invariants of these transformations similar to the distance between points and the angle between vectors.
Keywords: space with a multilinear form, cyclic algebra, cyclic space
Mots-clés : anticyclic space. 
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N. I. Guseva. Geometry of cyclic and anticyclic spaces. 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. 10-18. http://geodesic.mathdoc.fr/item/INTO_2023_222_a1/

[5] Burlakov M. P., Gamiltonovy algebry. Elementarnyi ocherk, Graf Press, M., 2017

[6] Burlakov M. P., Burlakov I. M., Guseva N. I., Ocherki ob algebrakh tsiklicheskikh chisel, Izd-vo «Kim», M., 2020

[7] Vishnevskii V. V., Shirokov A. P., Shurygin V. V., Gamiltonovy algebry, Izd-vo Kazan. un-ta, Kazan, 1985

[8] Garasko G. I., Nachala finslerovoi geometrii dlya fizikov, TETRA, M., 2009

[9] Guseva N. I., Burlakov M. P., Burlakov I. M., Elementarnaya geometriya v prostranstvakh nad algebrami, Intellekt-Tsentr, M., 2017

[10] Klein F., “Sravnitelnoe obozrenie noveishikh geometricheskikh issledovanii («Erlangenskaya programma»)”, Ob osnovaniyakh geometrii. Sbornik klassicheskikh rabot po geometrii Lobachevskogo i razvitiyu ee idei, ed. Norden A. P., GITTL, M., 1950

[11] Proskuryakov I. V., Sbornik zadach po lineinoi algebre, Lan, M., 2010

[12] Riman B., “O gipotezakh, lezhaschikh v osnovanii geometrii”, Albert Einshtein i teoriya gravitatsii, ed. Kuranskii E., Mir, M., 1979, 18–33