A classification of Ricci solitons as (K,μ)-contact metrics

Abstract

If a non-Sasakian (k,μ)-contact metric g is a non-trivial Ricci soliton on a (2n + 1)-dimensional smooth manifold M, then (M, g) is locally a threedimensional Gaussian soliton, or a gradient shrinking rigid Ricci soliton on the trivial sphere bundle S n.(4) × E n+1, or a non-gradient expanding Ricci soliton with k = 0,μ = 4. The last case occurs on a Lie group with a left invariant metric, especially for dimension 3, on Sol 3 regarded also as the group E(1,1) of rigid motions of the Minkowski 2-space.