Reduction of gradient Ricci soliton equations

Abstract

We consider gradient Ricci solitons conformal to a $n$-dimensional pseudo-Euclidean space and we completely describe the most general ansatz that reduces the resulting system of partial differential equations to a system of ordinary differential equations. As a consequence, the gradient Ricci solitons that arise from the reduced system are invariant under the action of either an $(n-1)$-dimensional translation group or the pseudo-orthogonal group acting on the corresponding $n$-dimensional pseudo-Euclidean space.

References in corpus (1)

• Gradient Ricci solitons on surfaces

Cited by in corpus (3)

• Rigidity results for Riemann solitons
• Static Einstein-Maxwell space-time invariant by translation
• Rigidity results on gradient Schouten solitons