Null hypersurfaces in indefinite nearly Kaehlerian Finsler spaces

  • Samuel Ssekajja University of KwaZulu-Natal
Keywords: Null hypersurfaces, Totally umbilic hypersurfaces, Indefinite Finsler spaces.


We study the geometry of null hypersurfaces, $M$, in indefinite nearly Kaehlerian Finsler space forms $\mathbb{F}^{2n}$. We prove new inequalities involving the point-wise vertical sectional curvatures of $\mathbb{F}^{2n}$, based on two special vector fields on an umbilic hypersurface. Such inequalities generalize some known results on null hypersurfaces of Kaehlerian space forms. Furthermore, under some geometric conditions, we show that the null hypersurface $(M, B)$, where $B$ is the local second fundamental form of $M$, is locally isometric to the null product $M_{D}\times M_{D'}$, where $M_{D}$ and $M_{D'}$ are the leaves of the distributions $D$ and $D'$ which constitutes the natural null-CR structure on $M$.