Lightlike Osserman submanifolds of semi-Riemannian manifolds

TL;DR

This paper explores lightlike Osserman submanifolds in semi-Riemannian manifolds, focusing on Jacobi operators, algebraic curvature tensors, and symmetry properties, with new examples and conditions for Osserman structures.

Contribution

It introduces the concept of lightlike Osserman submanifolds, provides examples of 2-degenerate Osserman metrics, and investigates symmetry properties related to Osserman conditions.

Findings

Introduction of lightlike Osserman submanifolds

Example of 2-degenerate Osserman metric

Results on symmetry properties of lightlike hypersurfaces

Abstract

In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We introduce the notion of lightlike Osserman submanifolds and an example of 2-degenerate Osserman metric is given. Finally we give some results of symmetry properties on lightlike hy- persurfaces from Osserman condition.