Characterizations and integral formulae for generalized quasi-Einstein metrics

2012/06/21 by Abdênago Barros, Ernani Ribeiro, Barros, Abdênago +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1206.4980

openalex publication_date 2012/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a space form with a well defined potential function f. Finally, we shall derive some integral formulae for such a class of compact manifolds which permit to obtain some rigidity results.

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