A condition of Osserman type, called the φ-null Osserman condition, is introduced and studied in the context of Lorentz globally framed f-manifolds. An explicit example shows the naturality of this condition in the setting of Lorentz 𝓢-manifolds. We prove that a Lorentz 𝓢-manifold with constant φ-sectional curvature is φ-null Osserman, extending a well-known result in the case of Lorentz Sasaki space forms. Then we state a characterization of a particular class of φ-null Osserman 𝓢-manifolds. Finally, some examples are examined.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-2-3,
author = {Letizia Brunetti},
title = {An Osserman-type condition on g.f.f-manifolds with Lorentz metric},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {123-141},
zbl = {1296.53044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-2-3}
}
Letizia Brunetti. An Osserman-type condition on g.f.f-manifolds with Lorentz metric. Annales Polonici Mathematici, Tome 111 (2014) pp. 123-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-2-3/