A note on proper curvature collineations in Bianchi type IV space-times

TL;DR

This paper investigates the conditions under which Bianchi type IV space-times admit proper curvature collineations, revealing that such collineations exist only in a specific case and form an infinite dimensional vector space.

Contribution

It provides a detailed analysis of proper curvature collineations in Bianchi type IV space-times using the Riemann matrix rank and direct integration, identifying the unique case of their existence.

Findings

Proper curvature collineations exist only in one specific case.

They form an infinite dimensional vector space.

The study uses the rank of the Riemann matrix and direct integration techniques.

Abstract

Curvature collineations of Bianchi type IV space-times are investigated using the rank of the 6X6 Riemann matrix and direct integration technique. From the above study it follows that the Bianchi type IV space-times possesses only one case when it admits proper curvature collineations. It is shown that proper curvature collineations form an infinite dimensional vector space.