# A note on proper affine symmetry in Bianchi types VIII and IX space-times

## TL;DR

This paper investigates proper affine symmetries in Bianchi types VIII and IX space-times, revealing that such symmetries occur only under a unique condition, using holonomy, decomposability, and Riemann matrix analysis.

## Contribution

It provides a comprehensive analysis of proper affine symmetries in Bianchi types VIII and IX space-times, identifying the specific condition under which these symmetries exist.

## Key findings

- Proper affine symmetry exists only under a unique condition in these space-times.
- Holonomy and Riemann matrix analysis are effective tools for studying symmetries.
- The study narrows down the circumstances for affine symmetries in complex cosmological models.

## Abstract

We consider the most general form of Bianchi types VIII and IX space-times for studying proper affine symmetry by using holonomy and decomposability, the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper affine symmetry in the above space-times it is shown that there exists only one possibilty when the above space-times admit proper affine vector field.

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Source: https://tomesphere.com/paper/1701.02217