José A. Oubiña

Reductive homogeneous pseudo-Riemannian manifolds

A classification of homogeneous pseudo-Riemannian structures and a characterization of each primitive class are obtained. Several examples are also given.

Homogeneous Lorentzian structures on the oscillator groups

Abstract. We obtain all the homogeneous pseudo-Riemannian structures on the oscillator groups equipped with a family of left-invariant Lorentzian metrics. Moreover, in the 4-dimensional case we determine all the corresponding reductive decompositions and groups of isometries.

Reductive decompositions and Einstein-Yang-Mills equations associated to the oscillator group

All of the homogeneous Lorentzian structures on the oscillator group equipped with a bi-invariant Lorentzian metric, and then the associated reductive pairs, are obtained. Some of them are solutions of the Einstein–Yang–Mills equations.

Homogeneous Kaehler and Sasakian structures related to complex hyperbolic space

We study homogeneous Kähler structures on a non-compact Hermitian symmetric space and their lifts to homogeneous Sasakian structures on the total space of a principal line bundle over it, and we analyze the case of the complex hyperbolic space.

Homogeneous Riemannian Structures on Berger 3-Spheres

The homogeneous Riemannian structures on the three-dimensional Berger spheres, their corresponding reductive decompositions and the associated groups of isometries are obtained. The Berger 3-spheres are also considered as homogeneous almost contact metric manifolds.

Homogeneous spin Riemannian manifolds with the simplest Dirac operator

Abstract We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds (M, g) which are traceless cyclic with respect to some quotient expression M = G/K and reductive decomposition 𝔤 = 𝔨 ⊕ 𝔪. Using transversally symmetric fibrations of noncompact type, we give a list of them.

The Lorentzian oscillator group as a geodesic orbit space

We prove that the four-dimensional oscillator group Os, endowed with any of its usual left-invariant Lorentzian metrics, is a Lorentzian geodesic (so, in particular, null-geodesic) orbit space with some of its homogeneous descriptions corresponding to certain homogeneous Lorentzian structures. Each time that Os is endowed with a suitable metric and an appropriate homogeneous Lorentzian structure, it is a candidate for constructing solutions in d-dimensional supergravity with at least 24 of the 32 possible supersymmetries.

A survey on homogeneous structures on the classical hyperbolic spaces

This is a survey on homogeneous Riemannian, Kahler or quaternionic Kahler structures on the real, complex or quaternionic hyperbolic spaces \(\mathbb {R}\mathrm {H}(n)\), \(\mathbb {C}\mathrm {H}(n)\) and \( \mathbb {H}\mathrm {H}(n)\), respectively.

CHERN-SIMONS FORMS OF PSEUDO-RIEMANNIAN HOMOGENEITY ON THE OSCILLATOR GROUP

We consider forms of Chern-Simons type associated to homogeneous pseudo-Riemannian structures. The corresponding secondary classes are a measure of the lack of a homogeneous pseudo-Riemannian space to be locally symmetric. In the present paper, we compute these forms for the oscillator group and the corresponding secondary classes of the compact quotients of this group.