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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 43–60 (Mi smj1821)  
This article is cited in 13 scientific papers (total in 13 papers)

Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras

V. V. Gorbatsevich

Moscow State Aviation Technological University
Full-text PDF (343 kB) Citations (13)
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Abstract: We study the algebraic conditions for all intrinsic metrics to be Finsler on a homogeneous space. These conditions were firstly found by Berestovskii in terms of Lie algebras and their subalgebras (the corresponding subalgebras will be called strong).
We obtain a description of the structure of strong subalgebras in semisimple solvable Lie algebras as well as Lie algebras of a general form. We also obtain some results on maximal strong subalgebras and Lie algebras with at least one strong subalgebra.
Keywords: invariant metric on a homogeneous space, intrinsic metric, Finsler metric, strong subalgebra.
Received: 18.08.2006
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 1, Pages 36–47
DOI: https://doi.org/10.1007/s11202-008-0004-1
Bibliographic databases:
UDC: 512.816
Language: Russian
Citation: V. V. Gorbatsevich, “Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras”, Sibirsk. Mat. Zh., 49:1 (2008), 43–60; Siberian Math. J., 49:1 (2008), 36–47
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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