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  • The metrizability problem for a symmetric affine connection on a manifold, invariant with respect to a group of diffeomorphisms G, is considered. We say that the connection is G-metrizable, if it is expressible as the Levi-Civita connection of a G-invariant metric field. In this paper we analyze the G-metrizability equations for the rotation group G = SO(3), acting canonically on three- and four dimensional Euclidean spaces. We show that the property of the connection to be SO(3)-invariant allows us to find complete explicit description of all solutions of the SO(3)-metrizability equations.
  • The metrizability problem for a symmetric affine connection on a manifold, invariant with respect to a group of diffeomorphisms G, is considered. We say that the connection is G-metrizable, if it is expressible as the Levi-Civita connection of a G-invariant metric field. In this paper we analyze the G-metrizability equations for the rotation group G = SO(3), acting canonically on three- and four dimensional Euclidean spaces. We show that the property of the connection to be SO(3)-invariant allows us to find complete explicit description of all solutions of the SO(3)-metrizability equations. (en)
Title
  • On metrizability of invariant affine connections
  • On metrizability of invariant affine connections (en)
skos:prefLabel
  • On metrizability of invariant affine connections
  • On metrizability of invariant affine connections (en)
skos:notation
  • RIV/61988987:17310/12:A1401A0L!RIV14-GA0-17310___
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  • P(GA201/09/0981), S
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  • 1
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  • 156274
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  • RIV/61988987:17310/12:A1401A0L
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  • Affine connection; metrizability; G-invariant (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • SG - Singapurská republika
http://linked.open...ontrolniKodProRIV
  • [370ECAF0DECC]
http://linked.open...i/riv/nazevZdroje
  • INT J GEOM METHODS M
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  • 9
http://linked.open...iv/tvurceVysledku
  • Krupka, Demeter
  • Tanaka, E.
issn
  • 0219-8878
number of pages
http://localhost/t...ganizacniJednotka
  • 17310
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