Four-dimensional D'Atri-Einstein spaces are locally symmetric

DOI10.1016/S0926-2245(99)00024-8zbMath0930.53028WikidataQ115337415 ScholiaQ115337415MaRDI QIDQ1303773

K. Paul Tod

Publication date: 22 September 1999

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

zbMATH Keywords

locally symmetricspinor formalismanti-selfdual Weyl tensorclassification of D'Atri spacesfour-dimensional D'Atri-Einstein manifolds

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Spin and Spin({}^c) geometry (53C27)

Related Items (11)

Immersions of \(r\)-almost Yamabe solitons into Riemannian manifolds ⋮ Characterization results and a sharp integral inequality for LW spacelike hypersurfaces in locally symmetric Lorentzian spaces ⋮ \(L\)-parabolic linear Weingarten spacelike hypersurfaces in a locally symmetric Einstein spacetime ⋮ Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space ⋮ \(r\)-almost Newton-Ricci solitons immersed into a Riemannian manifold ⋮ The Riemann extensions with cyclic parallel Ricci tensor ⋮ Unnamed Item ⋮ D'Atri spaces of Iwasawa type ⋮ Classification of 4-dimensional homogeneous D’Atri spaces ⋮ The Ledger curvature conditions and D'Atri geometry ⋮ Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds

Cites Work

• Interaction of tubes and spheres
• Volume-preserving geodesic symmetries on four-dimensional 2-Stein spaces
• Geodesic symmetries in spaces with special curvature tensors
• Divergence-preserving geodesic symmetries
• Symmetric Harmonic Spaces
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