Rigidity of weighted Einstein smooth metric measure spaces

2023/05/15 by Miguel Brozos‐Vázquez, Brozos-Vázquez, Miguel, Diego Mojón-Álvarez +1
Mathematics · Physics and Astronomy · #53B20 #53C21 #53C24 #53C25 #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.2305.08516

openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that either the underlying manifold is Einstein, or decomposes as a warped products in a specific way. Moreover, if the manifold is complete, then it either is a weighted analogue of a space form, or it belongs to a particular family of Einstein warped products.

Related

• Conformally weighted Einstein manifolds: the uniqueness problem
• Warped product Einstein metrics over spaces with constant scalar curvature
• Smooth metric measure spaces and quasi-Einstein metrics
• Rigidity of Quasi-Einstein Metrics
• On the characterization of Riemannian warped product Einstein metrics