An Osserman-type condition on $g.f.f$-manifolds with Lorentz metric

Volume 110 / 2014

Letizia Brunetti Annales Polonici Mathematici 110 (2014), 123-141 MSC: Primary 53C50; Secondary 53B30, 53C25. DOI: 10.4064/ap110-2-3


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.


  • Letizia BrunettiDepartment of Mathematics
    University of Bari “Aldo Moro”
    Via E. Orabona, 4
    70125 Bari, Italy

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