We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds and we use it to obtain an algebraic decomposition for the Riemannian curvature tensor of φ-null Osserman Lorentzian S-manifolds.
@article{bwmeta1.element.doi-10_2478_s11533-013-0331-8,
author = {Letizia Brunetti and Angelo Caldarella},
title = {Curvature properties of $\phi$-null Osserman Lorentzian S-manifolds},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {97-113},
zbl = {1300.53066},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0331-8}
}
Letizia Brunetti; Angelo Caldarella. Curvature properties of φ-null Osserman Lorentzian S-manifolds. Open Mathematics, Tome 12 (2014) pp. 97-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0331-8/
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