Geodesic
Geometry of linear algebras
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 Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 3-9

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In this paper, we consider spaces whose geometry is generated by a homogeneous function of degree $m\geq 2$ invariant under the action of some subgroup of the linear group of the given space. A general method is proposed and examples of realization of such spaces on linear algebras are given.
Keywords: fundamental form, linear algebra, vector bundle.
Mots-clés : motion group 
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     title = {Geometry of linear algebras},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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I. M. Burlakov. Geometry of linear algebras. 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 Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 3-9. http://geodesic.mathdoc.fr/item/INTO_2020_182_a0/