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Journal of Lie Theory 25 (2015), No. 4, 1023--1044
Copyright Heldermann Verlag 2015

Neutral Metrics on Four-Dimensional Lie Groups

Giovanni Calvaruso
Dip. di Matematica e Fisica, UniversitÓ del Salento, 73100 Lecce, Italy

Amirhesam Zaeim
Dept. of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

We consider four-dimensional Lie groups equipped with left-invariant metrics of signature (2,2). After describing the general structure of four-dimensional Lie algebras with a neutral inner product, we obtain a complete classification of left-invariant Einstein and Ricci-parallel metrics of neutral signature.

Keywords: Lie groups, left-invariant metrics, Einstein metrics, Ricci-parallel metrics, Ricci solitons.

MSC: 53C50, 53C15, 53C25

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