6533b7d9fe1ef96bd126d71e
RESEARCH PRODUCT
Homogeneous three-dimensional Riemannian spaces
Joan Josep FerrandoJuan Antonio Sáezsubject
PhysicsPure mathematicsIdeal (set theory)Physics and Astronomy (miscellaneous)010308 nuclear & particles physicsGroup (mathematics)Transitive actionFOS: Physical sciencesTransitive groupGeneral Relativity and Quantum Cosmology (gr-qc)01 natural sciencesGeneral Relativity and Quantum CosmologyHomogeneous0103 physical sciencesHomogeneous spaceMetric (mathematics)Mathematics::Differential Geometry010306 general physicsRicci curvaturedescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-04-04 |