${\mathcal{A}}^{\nabla}$-tensors on ligktlike hypersurfaces

Cyriaque Atindogbe (1) , Lionel Bérard Bergery (1)

1 IECN - Institut Élie Cartan de Nancy

This paper introduces $\anabla$-tensors on lightlike hypersurfaces $M^{n+1}$ of signature $(0,n)$, $(n\geq 1)$ and investigates on their properties in connection with the null geometry of $M$. In particular, we show that there is an interplay between existence of $\anabla$-tensors of certain type and lightlike warped product structures.

Mots clés: Lightlike hypersurface; screen distribution; $\anabla$-tensor; almost product structure; warped product

Domaines: Géométrie différentielle [math.DG]

Cyriaque Atindogbe, Lionel Bérard Bergery. ${\mathcal{A}}^{\nabla}$-tensors on ligktlike hypersurfaces. 2007. ⟨hal-00143469⟩