An Osserman-type condition on $g.f.f$-manifolds with Lorentz metric
Tom 110 / 2014
Annales Polonici Mathematici 110 (2014), 123-141
MSC: Primary 53C50; Secondary 53B30, 53C25.
DOI: 10.4064/ap110-2-3
Streszczenie
A condition of Osserman type, called the $\varphi $-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 $\mathcal {S}$-manifolds. We prove that a Lorentz $\mathcal {S}$-manifold with constant $\varphi $-sectional curvature is $\varphi $-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 $\varphi $-null Osserman $\mathcal {S}$-manifolds. Finally, some examples are examined.
