Journal ArticleDOI
Curvature Properties of Four-Dimensional Generalized Symmetric Spaces
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In this paper, the curvature of generalized symmetric spaces is described and the curvatures of four-dimensional generalized symmetrized spaces are classified in the Lorentzian case and in pseudo-Riemannian case.Abstract:
The curvature of four-dimensional generalized symmetric spaces is completely described. In particular, Einstein-like metrics on these spaces are classified. Interesting behaviours are found in the Lorentzian case and in one of the pseudo-Riemannian ones.read more
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Harmonicity of vector fields on four-dimensional generalized symmetric spaces
TL;DR: In this article, the authors completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields are critical points for the energy functional restricted to vector fields.
Journal ArticleDOI
Einstein-like warped product manifolds
TL;DR: In this paper, it was proved that the fiber manifold M2 of a warped product manifold M = M 1 × fM2 inherits the Einstein-like class type of M whereas the base manifold does not under some conditions.
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Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces
TL;DR: In this article, it was shown that a generalized symmetric space does not admit non-degenerate hypersurfaces with parallel second fundamental form unless it is locally symmetric.
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Symplectic, complex and Kähler structures on four-dimensional generalized symmetric spaces☆
TL;DR: In this paper, the full classification of invariant symplectic, (almost) complex and Kahler structures, together with their paracomplex analogues, on four-dimensional pseudo-Riemannian generalized symmetric spaces was obtained.
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Algebraic Ricci solitons of four-dimensional pseudo-Riemannian generalized symmetric spaces
Wafaa Batat,Kensuke Onda +1 more
TL;DR: In this paper, the algebraic Ricci solitons of four-dimensional generalized symmetric spaces were completely classified in terms of their Ricci-solitons' algebraic properties.
References
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Book
Generalized symmetric spaces
TL;DR: The classification of generalized symmetric Riemannian spaces in low dimensions and generalized affine symmetric spaces of solvable type was studied in this article, where generalized pointwise symmetric space was shown to be solvable.
Journal ArticleDOI
Homogeneous structures on three-dimensional Lorentzian manifolds
TL;DR: In this article, it was shown that any non-symmetric three-dimensional homogeneous Lorentzian manifold is isometric to a Lie group equipped with a left-invariant metric.
Book
Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor
TL;DR: Algebraic curvature tensors have a skew-symmetric curvature operator and a Jacobi operator controlling the eigenvalue structure as discussed by the authors, which is a special case of the Jacobi tensor.
Journal ArticleDOI
Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds
TL;DR: Abbena et al. as discussed by the authors completely classified three-dimensional homogeneous Lorentzian manifolds equipped with Einstein-like metrics, and showed that the Ricci tensor of (M, g) being cyclic-parallel is related to natural reductivity (respectively, symmetry) of (m, g).