The classification of 4-dimensional homogeneous D'Atri spaces revisited

DOI10.1016/J.DIFGEO.2006.04.001zbMath1121.53026OpenAlexW1972060811WikidataQ115357846 ScholiaQ115357846MaRDI QIDQ884011

Teresa Arias-Marco

Publication date: 13 June 2007

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2006.04.001

zbMATH Keywords

Riemannian manifoldD'Atri spacenaturally reductive Riemannian homogeneous space

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Local Riemannian geometry (53B20)

Related Items (4)

D'Atri spaces of type \(k\) and related classes of geometries concerning Jacobi operators ⋮ On inaudible curvature properties of closed Riemannian manifolds ⋮ The Riemann extensions with cyclic parallel Ricci tensor ⋮ Classification of 4-dimensional homogeneous D’Atri spaces

Cites Work

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• Curvatures of left invariant metrics on Lie groups
• Three- and four-dimensional Einstein-like manifolds and homogeneity
• The Ledger curvature conditions and D'Atri geometry
• Geodesic symmetries in spaces with special curvature tensors
• Four-dimensional Einstein-like manifolds and curvature homogeneity
• Divergence-preserving geodesic symmetries
• Classification of 4-dimensional homogeneous D’Atri spaces
• Infinitesimally homogeneous spaces

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