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

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

2011-12-05

arxiv.org/abs/1112.1050v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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

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