What question did this study set out to answer?

This research aims to explore the properties of compact m-quasi-Einstein manifolds with non-empty boundaries and Killing potentials.

On non-gradient quasi-Einstein manifolds with boundary and killing potentials

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Randomized trial explores scalar curvature implications of quasi-Einstein manifolds with boundary, indicating significant geometric properties.

This research aims to explore the properties of compact m-quasi-Einstein manifolds with non-empty boundaries and Killing potentials.
Introduction of the notion of compact m-quasi-Einstein manifolds where the potential vector field is not necessarily a gradient.
Proving that if the vector field is Killing, then the scalar curvature is constant.
Deriving a Chruściel-type inequality for m-quasi-Einstein manifolds with totally geodesic boundary.
If X is Killing, then scalar curvature S is constant.
If S is constant and X is Killing on the boundary of M, then X is Killing on M.
Derived results extend implications from previous studies under certain conditions.

Carvalho et al. (2026) studied this question.

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Randomized trial explores scalar curvature implications of quasi-Einstein manifolds with boundary, indicating significant geometric properties.