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.