1,721,085 research outputs found
From almost (para)-complex structures to affine structures on Lie groups
Full text linkLet G= H⋉ K denote a semidirect product Lie group with Lie algebra g= h⊕ k, where k is an ideal and h is a subalgebra of the same dimension as k. There exist some natural split isomorphisms S with S2= ± Id on g: given any linear isomorphism j: h→ k, we get the almost complex structure J(x, v) = (- j- 1v, jx) and the almost paracomplex structure E(x, v) = (j- 1v, jx). In this work we show that the integrability of the structures J and E above is equivalent to the existence of a left-invariant torsion-free connection ∇ on G such that ∇ J= 0 = ∇ E and also to the existence of an affine structure on H. Applications include complex, paracomplex and symplectic geometries.Fil: Calvaruso, Giovanni. Università del Salento; ItaliaFil: Ovando, Gabriela Paola. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin
Contact Lorentzian manifolds
No full textAbstractContact structures with associated pseudo-Riemannian metrics were studied by D. Perrone and the present author (2010) in [8]. We focus here on contact Lorentzian structures, emphasizing their relationship and analogies with respect to the Riemannian case
Harmonicity of vector fields on four-dimensional generalized symmetric spaces
No full textLet (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
Homogeneous paracontact metric three-manifolds
Full text linkThe complete classification of three-dimensional homogeneous
paracontact metric manifolds is obtained. In the symmetric
case, such a manifold is either flat or of constant sectional
curvature −1. In the non-symmetric case, it is a Lie group
equipped with a left-invariant paracontact metric structure
Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one
No full textFour-dimensional paraKahler Lie algebras: classification and geometry
No full textA paraK ̈ahler Lie algebra is an even-dimensional Lie algebra g endowed with a pair ,
where is a paracomplex structure and a pseudo-Riemannian metric, such that the fundamental
2-form is symplectic. We completely classify left-invariant paraK ̈ahler structures
on four-dimensional Lie algebras and then study the geometry of their paraK ̈ahler metri
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