2020/04/04 by Joan Josep Ferrando, Juan Antonio Sáez · 1 citation
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Geometry #Group (periodic table) #Homogeneous #Ideal (ethics) #Mathematical analysis #Mathematics #Metric (unit) #Physics #Pure mathematics #Ricci curvature #Tensor (intrinsic definition) #Transitive relation
paper · pdf · doi:10.1088/1361-6382/ab9880
openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are intrinsic, deductive, explicit and algorithmic, and they offer an IDEAL labeling of these geometries. It is shown that the transitive action of the group naturally falls into an unfolding of some of the ten types in the Bianchi–Behr classification. Explicit conditions, depending on the Ricci tensor, are obtained that characterize all these types.