Conformally flat Riemannian manifolds admitting a transitive group of isometries

DOI10.2748/TMJ/1178241040zbMath0311.53062OpenAlexW4240527495WikidataQ115227186 ScholiaQ115227186MaRDI QIDQ1219481

Hitoshi Takagi

Publication date: 1975

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178241040

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global Riemannian geometry, including pinching (53C20)

Related Items (19)

Curvature properties of Lorentzian manifolds with large isometry groups ⋮ Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension \(\leq 6\) ⋮ Rigidity of homogeneous gradient soliton metrics and related equations ⋮ Special ball-homogeneous spaces ⋮ Homogeneous Ricci almost solitons ⋮ Weakly-Einstein conditions over locally conformally flat Lorentzian three-manifolds ⋮ Automorphisms in generalized spaces ⋮ Structure of locally conformally flat manifolds satisfying some weakly-Einstein conditions ⋮ Homogeneity on three-dimensional contact metric manifolds ⋮ Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds ⋮ Groups of transformations of Riemannian manifolds ⋮ Conformally flat Riemannian manifolds admitting a transitive group of isometries. II ⋮ Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds ⋮ Conformally flat pseudo-symmetric spaces of constant type ⋮ Homogeneous Riemannian manifolds covered by \(S^m\times S^n\) ⋮ Locally conformally flat weakly-Einstein manifolds ⋮ Homogeneous conformal \(C\)-spaces in dimension four ⋮ Classification of conformally flat isoparametric submanifolds of Euclidean space ⋮ Four-dimensional pseudo-Riemannian homogeneous Ricci solitons

Cites Work

• Vincent's conjecture on Clifford translations of the sphere
• On conformally flat spaces satisfying a certain condition on the Ricci tensor
• On the Holonomy Group of the Conformally Flat Riemannian Manifold
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