Some triviality results for quasi-Einstein manifolds and Einstein warped products
Paolo Mastrolia, Michele Rimoldi
TL;DR
This paper establishes triviality results for Einstein warped products and quasi-Einstein manifolds by employing gradient estimates and Liouville-type theorems in weighted geometric settings.
Contribution
It introduces new techniques and assumptions to prove triviality results for these manifolds, extending classical theorems to weighted contexts.
Findings
Proved triviality results for Einstein warped products.
Developed gradient estimates for weighted Poisson equations.
Extended Liouville-type theorems to weighted manifolds.
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.
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