GENERALISED RICCI SOLITONS

Abstract. We introduce a class of overdetermined systems of partial differ-ential equations of finite type on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equations. These equations depend on three real parameters. For special values of the parameters they specialise to various im-portant classes of equations in differential geometry. Among them there are: the Ricci soliton equations, the vacuum near-horizon geometry equations in general relativity, special cases of Einstein-Weyl equations and their projective counter-parts, equations for homotheties and Killing’s equation. We also prolong the generalised Ricci soliton equations and, by computing differential constraints, we find a number of necessary conditions for a (pseudo)-Riemannian manifold (M, g) to locally admit non-trivial solutions to the gener-alised Ricci soliton equations in dimensions 2 and 3. The paper provides also a collection of explicit examples of generalised Ricc