Curvature properties of φ-null Osserman Lorentzian S-manifolds

Letizia Brunetti; Angelo Caldarella

Open Mathematics (2014)

  • Volume: 12, Issue: 1, page 97-113
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Letizia Brunetti, and Angelo Caldarella. "Curvature properties of φ-null Osserman Lorentzian S-manifolds." Open Mathematics 12.1 (2014): 97-113. <http://eudml.org/doc/269714>.

@article{LetiziaBrunetti2014,
abstract = {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.},
author = {Letizia Brunetti, Angelo Caldarella},
journal = {Open Mathematics},
keywords = {Osserman condition; Jacobi operator; Lorentzian S-manifold; Lorentz manifold; Lorentzian -manifold},
language = {eng},
number = {1},
pages = {97-113},
title = {Curvature properties of φ-null Osserman Lorentzian S-manifolds},
url = {http://eudml.org/doc/269714},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Letizia Brunetti
AU - Angelo Caldarella
TI - Curvature properties of φ-null Osserman Lorentzian S-manifolds
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 97
EP - 113
AB - 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.
LA - eng
KW - Osserman condition; Jacobi operator; Lorentzian S-manifold; Lorentz manifold; Lorentzian -manifold
UR - http://eudml.org/doc/269714
ER -

References

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