arXiv subjects

Letizia Brunetti

Publications and source records attributed to Letizia Brunetti.

6 recordsLinked to original sources

arXiv2012

An Osserman-type condition on $g.f.f$-manifolds with Lorentz metric

A condition of Osserman type, called $ϕ$-null Osserman condition, is introduced and studied in the context of Lorentz globally framed $f$-manifolds. An explicit example shows the naturalness of this condition in the setting of Lorentz $\mathcal{S}$-manifolds. We prove that a Lorentz $\mathcal{S}$-manifold with constant $ϕ$-sectional curvature is $ϕ$-null Osserman, extending a result stated for Lorentz Sasaki space forms. Then we state some characterizations for a particular class of $ϕ$-null Osserman $\cal{S}$-manifolds. Finally, some examples are examined.

math.DG↗

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↗

arXiv2012

The $η$-Einstein condition on indefinite s-manifolds

An $η$-Einstein condition is introduced in the context of indefinite g.f.f-manifolds, and a few Schur-type lemmas for indefinite S-manifolds are provided.

math.DG↗

arXiv2008

Curvature of a class of indefinite globally framed $f$-manifolds

We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and $ϕ$-sectional curvature of indefinite almost $\mathcal{S}$-manifolds and state an expression of the curvature tensor field for the indefinite $\mathcal{S}$-space forms. We analyse the sectional curvature of indefinite $\mathcal{S}$-manifold in which the number of the spacelike characteristic vector fields is equal to that of the timelike characteristic vector fields. Some examples are also described.

math.DG↗

arXiv2008

Lightlike hypersurfaces in indefinite $\mathcal{S}$-manifolds

In a metric $g.f.f$-manifold we study lightlike hypersurfaces $M$ tangent to the characteristic vector fields, and owing to the presence of the $f$-structure, we determine some decompositions of $TM$ and of a chosen screen distribution obtaining two distributions invariant with respect to the structure. We discuss the existence of a $g.f.f$-structure on a lightlike hypersurface and, under suitable hypotheses, we obtain an indefinite $\mathcal{S}$-structure on the leaves of an integrable distribution. The existence of totally umbilical lightlike hypersurfaces of an indefinite $\mathcal{S}$-space form is also discussed. Finally, we explicitely describe a lightlike hypersurface of an indefinite $\mathcal{S}$-manifold.

math.DG↗