On Metrizability of Invariant Affine Connections

Details On Metrizability of Invariant Affine Connections On Metrizability of Invariant Affine Connections

2011-11-13

arxiv.org/abs/1111.3009v1

IJGMMP, Vol. 9, No. 1 (2012), 1250014

Physics

Mathematical Physics

17 pages, To appear in IJGMMP vol.9 No.1 (2012)

Scientific paper

10.1142/S0219887812500144

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.

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