Let (M, g) be a smooth manifold M endowed with a metric g. A large class of differential operators in differential geometry is intrinsically defined by means of the dual metric g ∗ on the dual bundle T M ∗ of 1-forms on M. If the metric g is (semi [...]
ATINDOGBE COMLAN CYRIAQUE [1], TOSSA JOEL [3], EZIN JEAN-PIERRE [2],
We study and characterize a class of lightlike hypersurfaces in Lorentzian manifolds of constant curvature, that satisfy Einstein equation. Integrability and characterization results are established. [...]
ATINDOGBE COMLAN CYRIAQUE [1], EZIN JEAN-PIERRE [2], TOSSA JOEL [3],
This paper deals with results concerning the relative nullity foliation of the screen distribution of a lightlike Einstein hypersurface $M$ in the Lorentzian space $\mathbb{R}^{n+2}_{1}$ and gives a characterization theorem for t [...]
ATINDOGBE COMLAN CYRIAQUE [1], EZIN JEAN-PIERRE [2], TOSSA JOEL [3],
Degenerate submanifolds of pseudo-Riemannian manifolds are quite difficult to study because there is no preferred connection when the sub- manifold is not totally geodesic. For the particular case of degenerate totally umbilical hypersurfaces, we [...]
Recently, the concept of induced scalar curvature of lightlike hypersurfaces is introduced, restricting on a special class of the latter. This paper removes some of these constraints and constructs this scalar quantity by an approach that is consi [...]
This paper introduces Gray-tensors on lightlike hypersurfaces M n+1 of signature (0, n), (n ≥ 1) and investigates on their basic properties in connec- tion with their null geometry. In particular, we show that there is an interplay between existen [...]
ATINDOGBE COMLAN CYRIAQUE [1], BERARD BERGERY LIONEL [2], TOSSA JOEL [3],
We study pseudo-Jacobi operators associated to algebraic curvature maps on lightlike hypersurfaces M and investigate conditions for an induced Riemann curvature tensor to be an algebraic curvature map on M. Two examples are provided with explicit [...]
In this paper we construct and study a Blaschke type normalization on the lightlike hypersurface immersions with 1-degenerate second fundamental form. We discuss basic examples and establish fundamental equations for this canonical transversal vec [...]
In a recent paper [C. Atindogbé, Scalar curvature on lightlike hypersurfaces, Appl. Sci. 11 (2009) 9–18], the present author considered the concept of extrinsic (induced) scalar curvature on lightlike hypersurfaces. This scalar quantity has been st [...]
We give a sufficient condition for a lightlike isotropic submanifold M, of dimension n, which is not totally geodesic in a semi-Riemannian manifold of constant curvature c and of dimension n + p(n < p), to admit a reduction of codimension. We show [...]