On complete gradient Schouten solitons

Abstract

In this paper, we prove an optimal inequality between the potential function of a complete Schouten soliton and the norm of its gradient. We also prove that these metrics have bounded scalar curvature of defined sign. As an application, we prove that the potential function of a Shrinking Schouten soliton grows linearly and provide optimal estimates for the growth of the volume of geodesic balls, without any further assumption.

Minor corrections

Cited by in corpus (4)

• Rigidity results for Riemann solitons
• Geometric and analytic results for Einstein solitons
• Diameter estimation of gradient $\rho$-Einstein solitons
• Rigidity results on gradient Schouten solitons