Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

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.