# On the geometry of lightlike submanifolds of indefinite statistical manifolds

## TL;DR

This paper investigates the properties of lightlike submanifolds within indefinite statistical manifolds, establishing conditions for their statistical structure and analyzing curvature and Ricci tensor symmetry.

## Contribution

It provides new conditions under which lightlike submanifolds of indefinite statistical manifolds are statistical, extending classical submanifold theory to indefinite settings.

## Key findings

- Conditions for lightlike submanifolds to be statistical
- Expression of statistical sectional curvature
- Criteria for symmetry of induced statistical Ricci tensor

## Abstract

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.