On contact screen conformal null submanifolds

TL;DR

This paper investigates the properties of contact screen conformal null submanifolds within indefinite Sasakian manifolds, establishing their existence in specific curvature conditions and characterizing their geometric features.

Contribution

It introduces the concept of contact screen conformal null submanifolds in indefinite Sasakian manifolds and provides characterization results, including their existence in certain space forms.

Findings

Indefinite Sasakian manifolds do not admit certain null submanifolds tangent to the structure vector field.

Contact screen conformal null submanifolds exist in indefinite Sasakian space forms with constant holomorphic sectional curvature -3.

Characterization theorems for these null submanifolds are established.

Abstract

First, we prove that indefinite Sasakian manifolds do not admit any screen conformal $r$-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen conformal} $r$-null submanifold of indefinite Sasakian manifolds. Several characterization results, on the above class of null submanifolds, are proved. In particular, we prove that such null submanifolds exist in indefinite Sasakian space forms of constant holomorphic sectional curvatures of $-3$.