Lightlike submanifolds of metallic semi-Riemannian manifolds

Abstract

Our aim in this paper is to investigate some special types of lightlike submanifolds in metallic semi-Riemannian manifolds. We study invariant lightlike submanifolds and screen semi-invariant lightlike hypersurfaces of metallic semi-Riemannian manifolds and give examples. We obtain some conditions for the induced connection to be a metric connection and present integrability conditions for the distributions involved in the definitions of such types.

Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor

“…Moreover, properties of metallic and Golden warped product Riemannian manifolds were presented in the two previous works of the authors [13,14]. Lately, the study of submanifolds in metallic Riemannian manifolds has been continued by many authors [15][16][17], which introduced the notion of a lightlike submanifold of a metallic semi-Riemannian manifold.…”

Curvature Tensors of Screen Semi-invariant Half-Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter-Symmetric Non-metric Connection

“…Since the tools used to investigate the geometry of submanifolds in a Riemannian manifold are not favourable in semi-Riemannian cases, so the lightlike (degenerate) geometry plays a pivotal role in the study of such structures. Within this framework, the invariant submanifolds for golden semi-Riemannnian manifolds were investigated by [4] and for metallic semi-Riemannian manifolds with metric connection by [18]. One more interesting class of submanifolds, namely screen semi-invariant lightlike submanifold was established by [3] for the semi-Riemannian product manifold.…”