arXiv subjects

Angelo V. Caldarella

Publications and source records attributed to Angelo V. Caldarella.

5 recordsLinked to original sources

arXiv2012

Curvature properties of $ϕ$-null Osserman Lorentzian $\mathcal{S}$-manifolds

We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian $\mathcal{S}$-manifold $M$ and the Jacobi operators with respect to particular spacelike unit vectors on $M$. We study the number of the eigenvalues of such operators in a $ϕ$-null Osserman Lorentzian $\mathcal{S}$-manifold, under suitable assumptions on the dimension of the manifold. Then, we generalize a curvature characterization, previously obtained by the first author for Lorentzian $ϕ$-null Osserman $\mathcal{S}$-manifolds with exactly two characteristic vector fields, to the case of those with an arbitrary number of characteristic vector fields.

math.DG↗

arXiv2012

Principal torus bundles of Lorentzian S-manifolds and the ϕ-null Osserman condition

The main result we give in this brief note relates, under suitable hypotheses, the ϕ-null Osserman, the null Osserman and the classical Osserman conditions to each other, via semi-Riemannian submersions as projection maps of principal torus bundles arising from a Lorentzian S-manifold.

math.DG↗

arXiv2008

On paraquaternionic submersions between paraquaternionic Kähler manifolds

In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic Kähler non locally hyper paraKähler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.

math.DG↗

arXiv2008

Mixed metric 3-contact manifolds and paraquaternionic Kähler manifolds

We study manifolds endowed with mixed metric 3--contact structures, proving that the distribution spanned by the Reeb vector fields is integrable, with totally geodesic integral manifolds, of constant sectional curvature $k=\pm1$. We also prove a result of projectability of such structures onto paraquaternionic Kählerian structures.

math.DG↗

arXiv2008

Mixed 3-Sasakian structures and curvature

In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the identity between the class of mixed 3-Sasakian structures and the class of mixed metric 3-contact structures.

math.DG↗