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

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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 Berestovskiĭ 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.

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Authors and Affiliations

  1. Moscow State Technological University, Moscow, Russia

    V. V. Gorbatsevich

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  1. V. V. Gorbatsevich
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Correspondence to V. V. Gorbatsevich.

Additional information

Original Russian Text Copyright © 2008 Gorbatsevich V. V.

The author was supported by the Russian Foundation for Basic Research (Grant 04–01–00647).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 43–60, January–February, 2008.

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Gorbatsevich, V.V. Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras. Sib Math J 49, 36–47 (2008). https://doi.org/10.1007/s11202-008-0004-1

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  • DOI: https://doi.org/10.1007/s11202-008-0004-1

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