Some triviality results for quasi-Einstein manifolds and Einstein warped products

Abstract

In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for solutions of weighted Poisson-type equations and adaptations to the weighted setting of some Liouville-type theorems.Comment: 15 pages, fixed minor mistakes in Section