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
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 
@article{INTO_2020_182_a0,
     author = {I. M. Burlakov},
     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},
     pages = {3--9},
     year = {2020},
     volume = {182},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_182_a0/}
}
TY  - JOUR
AU  - I. M. Burlakov
TI  - Geometry of linear algebras
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 3
EP  - 9
VL  - 182
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_182_a0/
LA  - ru
ID  - INTO_2020_182_a0
ER  - 
%0 Journal Article
%A I. M. Burlakov
%T Geometry of linear algebras
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 3-9
%V 182
%U http://geodesic.mathdoc.fr/item/INTO_2020_182_a0/
%G ru
%F INTO_2020_182_a0
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/

[2] Burlakov I. M., Burlakov M. P., Geometricheskie struktury lineinykh algebr, LAP LAMBERT, 2016

[3] Burlakov M. P., Gamiltonovy algebry, Graf Press, M., 2006

[4] Burlakov M. P., Algebraicheskie metody v geometricheskoi fizike, Groznyi, 1985

[5] Garasko G. I., Nachala finslerovoi geometrii dlya fizikov, TETRU, M., 2009

[6] Klein F., Elementarnaya matematika s tochki zreniya vysshei, Nauka, M., 1987

[7] Mischenko A. S., Vektornye rassloeniya i ikh primeneniya, Nauka, M., 1984

[8] Rozenfeld B. A., Neevklidovy geometrii, GITTL, M., 1955 | MR