Rigidity results on gradient Schouten solitons

Abstract

In this paper we consider $\rho$-Einstein solitons of type $M=\left(B^n,g^{\ast }\right)\times (F^m,g_F)$, where $\left(B^n,g^{\ast }\right)$ is conformal to a pseudo-Euclidean space and invariant under the action of the pseudo-orthogonal group, and $\left(F^m,g_F\right)$ is an Einstein manifold. We provide all the solutions for the gradient Schouten soliton case. Moreover, in the Riemannian case, we prove that if $M=\left(B^n,g^{\ast }\right)\times (F^m,g_F)$ is a complete gradient Schouten soliton then $\left(B^n,g^{\ast }\right)$ is isometric to ${\mathbb{S}}^{n-1}\times \mathbb{R}$ and $F^m$ is a compact Einstein manifold.

References in corpus (1)

• On complete gradient Schouten solitons