Rigid properties of quasi-almost-Einstein metrics

Abstract

In this paper, quasi-almost-Einstein metrics on complete manifolds are studied. Two examples are given and several formulas are established. With the help of these formulas, the author proves rigid results on compact or noncompact manifolds, in which some basic tools, such as the weighted volume comparison theorem and the weak maximum principle at infinity, are used. A lower bound estimate for the scalar curvature is also obtained.

Keywords

Quasi-almost-Einstein metric / Potential function / Gradient estimate / Rigid property

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