Radical transversal lightlike hypersurfaces of almost complex manifolds with Norden metric

TL;DR

This paper introduces and studies radical transversal lightlike hypersurfaces in almost complex manifolds with Norden metric, revealing unique geometric properties and their relations to non-degenerate hypersurfaces.

Contribution

It defines a new class of lightlike hypersurfaces specific to Norden metric manifolds and explores their geometric properties and relations to other hypersurfaces.

Findings

Existence of unique screen distribution for these hypersurfaces

Symmetric Ricci tensor property in Kaehler Norden manifolds

Examples illustrating the hypersurfaces' properties

Abstract

In this paper we introduce radical transversal lightlike hypersurfaces of almost complex manifolds with Norden metric. The study of these hypersurfaces is motivated by the fact that for indefinite almost Hermitian manifolds this class of lightlike hypersurfaces does not exist. We also establish that radical transversal lightlike hypersurfaces of almost complex manifolds with Norden metric have nice properties as a unique screen distribution and a symmetric Ricci tensor of the considered hypersurfaces of Kaehler manifolds with Norden metric. We obtain new results about lightlike hypersurfaces concerning to their relations with non-degenerate hypersurfaces of almost complex manifolds with Norden metric. Examples of the considered hypersurfaces are given.