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

Letizia Brunetti¹

¹ Department of Mathematics University of Bari “Aldo Moro” Via E. Orabona, 4 70125 Bari, Italy

Annales Polonici Mathematici, Tome 110 (2014) no. 2, pp. 123-141

Résumé

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.

Détail

DOI : 10.4064/ap110-2-3

Keywords: condition osserman type called varphi null osserman condition introduced studied context lorentz globally framed f manifolds explicit example shows naturality condition setting lorentz mathcal manifolds prove lorentz mathcal manifold constant varphi sectional curvature varphi null osserman extending well known result lorentz sasaki space forms state characterization particular class varphi null osserman mathcal manifolds finally examples examined