The Ledger curvature conditions and D'Atri geometry

DOI10.1016/S0926-2245(99)00026-1zbMath0944.53025OpenAlexW1994301774WikidataQ115337413 ScholiaQ115337413MaRDI QIDQ1807644

Paul Tod, Henrik Pedersen

Publication date: 8 February 2000

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

Full work available at URL: https://doi.org/10.1016/s0926-2245(99)00026-1

zbMATH Keywords

D'Atri spacecyclic Ricci-parallelLedger condition

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Geodesics in global differential geometry (53C22)

Related Items (16)

Curvature operators and generalizations of symmetric spaces in Lorentzian geometry ⋮ Killing and conformal Killing tensors ⋮ Four-Dimensional Homogeneous Generalizations of Einstein Metrics ⋮ The classification of 4-dimensional homogeneous D'Atri spaces revisited ⋮ Isoparametric foliation and a problem of Besse on generalizations of Einstein condition ⋮ D'Atri spaces and the total scalar curvature of hemispheres, tubes and cylinders ⋮ Riemannian 3-metrics with a generic Codazzi Ricci tensor ⋮ Some examples of the behaviour of conformal geodesics ⋮ D'Atri spaces of type \(k\) and related classes of geometries concerning Jacobi operators ⋮ Curvature properties of twistor spaces ⋮ On inaudible curvature properties of closed Riemannian manifolds ⋮ The Riemann extensions with cyclic parallel Ricci tensor ⋮ Einstein condition and twistor spaces of compatible partially complex structures ⋮ D'Atri spaces of Iwasawa type ⋮ \(\mathcal{A}\)-manifolds on a principal torus bundle over an almost Hodge \(\mathcal{A}\)-manifold base ⋮ Classification of 4-dimensional homogeneous D’Atri spaces

Cites Work

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• Non-homogeneous Kähler-Einstein metrics on compact complex manifolds. II
• Four-dimensional D'Atri-Einstein spaces are locally symmetric
• Geodesic symmetries in spaces with special curvature tensors
• Divergence-preserving geodesic symmetries
• Symmetric Harmonic Spaces
• Riemannian Submersions, Four-Manifolds and Einstein-Weyl Geometry
• Curvature invariants, differential operators and local homogeneity
• K-contact A-manifolds
• Infinitesimally homogeneous spaces

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