We study some properties of a lightlike hypersurface M , of a Lorentzian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We prove that some specified aspects of the null geometry of M reduce to the Rie [...]
DUGGAL KRISHAN LAL [2], ATINDOGBE COMLAN CYRIAQUE [1], DUGGAL KRISHAN LAL [2],
In this paper, the pseudo-inversion of degenerate metric is considered. We extend Szabó operators associated to algebraic covariant derivative curvature maps (tensors) to lightlike hypersurfaces. Some examples are given with explicit determination [...]
ATINDOGBE COMLAN CYRIAQUE [1], LUNGIAMBUDILA OSCAR [2], TOSSA JOEL [3],
In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Riemann curvature tensor to be an algebraic curvature tensor on M. We introduce the noti [...]
ATINDOGBE COMLAN CYRIAQUE [1], LUNGIAMBUDILA OSCAR [2], TOSSA JOEL [0],
We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein–Weyl screen st [...]
ATINDOGBE COMLAN CYRIAQUE [1], BERARD BERGERY LIONEL [0], OGOUYANDJOU KOLADÉ SIMPLICE EPHREM CARLOS [3],
We show that on a non-minimal lightlike hypersurface with nullity degree 1 , there exists a unique null transversal (normalizing) vector eld with prescribed calibrated divergence, for which the induced connection and the Levi-Civita connection of [...]
In this paper, the induced Ricci tensor and the extrinsic scalar curvature on lightlike submanifolds are obtained. This scalar quantity extend the result given by C. Atindogbe in [1]. An example of extrinsic scalar curvature on one class of 2 -dege [...]
ATINDOGBE COMLAN CYRIAQUE [1], LUNGIAMBUDILA OSCAR [2], TOSSA JOEL [3],
Abstract. Let (M, F ) be a compact Finsler manifold of hyperbolic type, M̃ F be its universal Finslerian covering and α F the critical exponent of the group of the deck transformations of M̃ F . In this paper we prove the existence of an α F -Buse [...]
ATINDOGBE COMLAN CYRIAQUE [1], OGOUYANDJOU KOLADÉ SIMPLICE EPHREM CARLOS [2], TOSSA JOEL [3],
In this paper, we study lightlike hypersurfaces with parallel screen shape operator. The main result is a characterization theorem for lightlike with parallel screen shape of a Lorentzian space form. [...]
ATINDOGBE COMLAN CYRIAQUE [2], HAROUNA MAHAMANE MAHI [1], TOSSA JOEL [0],
Any rigged null hypersurface is provided with two shape operators: with respect to the rigging and the rigged vector fields respectively. The present paper deals with the Newton transformations built on both of them and establishes related curvatur [...]
This paper deals with a family of Osserman lightlike hypersurfaces (M u ) of a class of Lorentzian manifolds M̄ such that its each null normal vector is defined on some open subset of M̄ around M u . We prove that a totally umbilical family of ligh [...]