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Classification of Left-Invariant Riemannian Metrics on Nonunimodular 4-Dimensional Lie Groups

A classification, up to automorphism, of left-invariant Riemannian metrics on four-dimensional simply connected nonunimodular Lie groups, obtained by classifying inner products on the corresponding nonunimodular Lie algebras modulo the pullback action of the automorphism group, with the moduli space realized as the orbit space of that action.

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Classiﬁcation of left invariant Riemannian metrics on nonunimodular 4-dimensional Lie groups Malika

Classifies, up to automorphism, the left-invariant Riemannian metrics on four-dimensional simply connected nonunimodular Lie groups. Because a left-invariant metric is determined by an inner product …