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

Abstract

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 $\varphi$-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 $\varphi$-null Osserman $\mathcal{S}$-manifolds with exactly two characteristic vector fields, to the case of those with an arbitrary number of characteristic vector fields.

15 pages; signs corrected on page 8, reference added

References in corpus (1)

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