Algebraic properties of curvature operators in Lorentzian manifolds with large isometry groups.
Harmonicity of vector fields on four-dimensional generalized symmetric spaces
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of the Lie algebra g of G. We 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. Vector fields defining harmonic maps are also classified, and the energy of these vector fields is explicitly calculated.
A complete classification of four-dimensional paraKähler Lie algebras
We consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.
Conformally flat pseudo-symmetric spaces of constant type
We give the complete classification of conformally flat pseudo-symmetric spaces of constant type.
Conformally flat Lorentzian three-spaces with various properties of symmetry and homogeneity
We study conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric. Their complete classification is obtained under hypotheses of local homogeneity and curvature homogeneity. Moreover, examples which are not curvature homogeneous are described.
Conformally flat semi-symmetric spaces
We obtain the complete classification of conformally flat semi-symmetric spaces.
On the Ricci operator of locally homogeneous Lorentzian 3-manifolds
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
Cosymplectic and α-cosymplectic Lie algebras
-natural metrics of constant curvature on unit tangent sphere bundles
We completely classify Riemannian -natural metrics of constant sectional curvature on the unit tangent sphere bundle of a Riemannian manifold . Since the base manifold turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian -natural metric on the unit tangent sphere bundle of a Riemannian surface.
Some examples of harmonic maps for -natural metrics
We produce new examples of harmonic maps, having as source manifold a space of constant curvature and as target manifold its tangent bundle , equipped with a suitable Riemannian -natural metric. In particular, we determine a family of Riemannian -natural metrics on , with respect to which all conformal gradient vector fields define harmonic maps from into .
Three-dimensional curvature homogeneous hypersurfaces
This paper is motivated by the open problem whether a three-dimensional curvature homogeneous hypersurface of a real space form is locally homogeneous or not. We give some partial positive answers.
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