A note on proper curvature collineations in Bianchi types VI_{0} and VII_{0} space-times

TL;DR

This paper investigates proper curvature collineations in Bianchi types VI_{0} and VII_{0} space-times, revealing they form an infinite dimensional vector space when such collineations exist, using Riemann matrix rank and direct integration.

Contribution

It provides a detailed analysis of proper curvature collineations in specific Bianchi space-times, showing their infinite dimensional nature under certain conditions.

Findings

Proper curvature collineations form an infinite dimensional vector space.

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

Applicable to Bianchi types VI_{0} and VII_{0} space-times.

Abstract

We study proper curvature collineations in the most general form of the Bianchi types VI_{0} and VII_{0} space-times using the rank of the 6X6 Riemann matrix and direct integration technique. It is shown that when the above space-times admit proper curvature collineations, they form an infinite dimensional vector space.