On the Geometry of the Null Tangent Bundle of a Pseudo-Riemannian Manifold

Abstract

When we consider a non-definite pseudo-Riemannian manifold, we obtain lightlike tangent vectors that constitute the null tangent bundle, whose fibers are lightlike cones in the corresponding tangent spaces. In this paper, we define and study a class of “g-natural” metrics on the tangent bundle of a pseudo-Riemannian manifold and we investigate the geometry of the null tangent bundle as a lightlike hypersurface equipped with an induced g-natural metric.