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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, Volume 154, Book 4, Pages 146–155 (Mi uzku1165)  
This article is cited in 1 scientific paper (total in 1 paper)

Left-invariant metrics on a tensor bundle of type $(2,0)$ over a Lie group

N. A. Opokina

Kazan (Volga Region) Federal University
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Abstract: In this paper, we construct vertical and horizontal lifts of left-invariant vector fields. We establish necessary and sufficient conditions for the horizontal lift of a left-invariant vector field to be a left-invariant field. From a left-invariant metric on $G$, we build a left-invariant metric on $T^2_0G$.
Keywords: left-invariant metric, tensor bundle over a Lie group, vertical and horizontal lifts, left-invariant vertical and horizontal distributions.
Received: 18.06.2012
Document Type: Article
UDC: 514.762.33
Language: Russian
Citation: N. A. Opokina, “Left-invariant metrics on a tensor bundle of type $(2,0)$ over a Lie group”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 154, no. 4, Kazan University, Kazan, 2012, 146–155
Citation in format AMSBIB
\Bibitem{Opo12}
\by N.~A.~Opokina
\paper Left-invariant metrics on a~tensor bundle of type $(2,0)$ over a~Lie group
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2012
\vol 154
\issue 4
\pages 146--155
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1165}
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  • https://www.mathnet.ru/eng/uzku/v154/i4/p146
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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