Geometry of lightlike hypersurfaces of a statistical manifold

TL;DR

This paper investigates the geometric properties of lightlike hypersurfaces within statistical manifolds, revealing that while the hypersurface itself isn't statistical under induced connections, its screen distribution is, and exploring related geometric relations.

Contribution

It introduces the canonical statistical structure of the screen distribution and analyzes the relations between dual connections on lightlike hypersurfaces in statistical manifolds.

Findings

Screen distribution has a canonical statistical structure

Relations between induced geometric objects with dual connections are established

Induced Ricci tensors are computed for lightlike hypersurfaces

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.