Riemannian 3-metrics with a generic Codazzi Ricci tensor

DOI10.1007/s10711-010-9532-5zbMath1218.53015OpenAlexW2015604311MaRDI QIDQ2430729

Giovanni Calvaruso

Publication date: 8 April 2011

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-010-9532-5

zbMATH Keywords

Einstein-like metricsconformally flat metricsCodazzi Ricci tensor

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Local Riemannian geometry (53B20)

Related Items

Gray’s decomposition on doubly warped product manifolds and applications ⋮ Einstein-like warped product manifolds ⋮ Rigidity of noncompact manifolds with cyclic parallel Ricci curvature

Cites Work

• Unnamed Item
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Classification of certain compact Riemannian manifolds with harmonic curvature and non-parallel Ricci tensor
• Existence of metrics with prescribed Ricci curvature: Local theory
• Einstein-like manifolds which are not Einstein
• Three- and four-dimensional Einstein-like manifolds and homogeneity
• Metrics with prescribed Ricci curvature of constant rank. I: The integrable case
• On Riemannian 3-manifolds with distinct constant Ricci eigenvalues
• The Ledger curvature conditions and D'Atri geometry
• Three-dimensional Ivanov–Petrova manifolds
• The Yamabe problem
• The equation of prescribed Ricci curvature
• A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ₁= ρ₂≠ ρ₃
• Three-dimensional Riemannian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3