Geometry of lightlike hypersurfaces of a statistical manifold

Abstract

Lightlike hypersurfaces of a statistical manifold are studied. It is shown that a lightlike hypersurface of a statistical manifold is not a statistical manifold with respect to the induced connections, but the screen distribution has a canonical statistical structure. Some relations between induced geometric objects with respect to dual connections in a lightlike hypersurface of a statistical manifold are obtained. An example is presented. Induced Ricci tensors for lightlike hypersurface of a statistical manifold are computed.

Main Curvatures Identities on Lightlike Hypersurfaces of Statistical Manifolds and Their Characterizations

“…In addition, both the second fundamental forms' B and B * are symmetric and bilinear, called the imbedding curvature tensors of the submanifold for ∇ and ∇, respectively. We note that a lightlike hypersurface of a statistical manifold does not need to be a statistical manifold with respect to ∇ and ∇ * [12].…”

“…[10,11]. In degenerate cases, lightlike hypersurfaces of statistical manifolds were introduced by the first author and M. M. Tripathi [12]. In addition, statistical lightlike hypersurfaces were studied by V. Jain, A. P. Singh, and R. Kumar in Ref.…”