What question did this study set out to answer?

The research aims to analyze compact quasi-Einstein manifolds under the condition of zero radial Weyl curvature.

July 31, 2026Open Access

On compact quasi-Einstein metrics with zero radial Weyl curvature

HBH. BaltazarUniversidade Federal do Piauí JCJ. CarvalhoUniversidade Federal do Piauí XCX. ChenChina University of Petroleum, Beijing

Key Points

The research aims to analyze compact quasi-Einstein manifolds under the condition of zero radial Weyl curvature.
Study of the isometric properties of quasi-Einstein manifolds.
Prove connections to standard hemispheres and warped products.
Focus on manifolds with boundary and nonnegative Ricci curvature.
Demonstrates that compact quasi-Einstein manifolds are isometric, up to scaling, to either the standard hemisphere or a specific warped product configuration.
Verifies that the warped product takes the form of a metric related to Einstein metrics with nonnegative Ricci curvature.

Abstract

Abstract The aim of this paper is to study compact quasi-Einstein manifolds with boundary satisfying the zero radial Weyl curvature condition. More precisely, we prove that a compact quasi-Einstein manifold (M^n, g, f), n 5, with zero radial Weyl curvature is isometric, up to scaling, to either the standard hemisphere S^n+, or a warped product g=dt^2+ ^2g₋, and f=f (t), where g₋ is Einstein with nonnegative Ricci curvature.

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