On the geometry of Einstein-type manifolds with some structural conditions

2022/03/30 by Gabjin Yun, Yun, Gabjin, Seungsu Hwang +1
Mathematics · Physics and Astronomy · #53C20 #53C25 #53C43 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Fixed Point Theorems Analysis #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2203.16146

openalex publication_date 2022/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation. We show various rigidity results of Einstein-type manifolds under assumptions of several curvature conditions.

Related

• Geometry of Einstein-type manifolds with boundary
• Special Einstein's equations on Kähler manifolds
• Characterizations and integral formulae for generalized quasi-Einstein metrics
• Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds
• Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds