A note on classification of proper homothetic vector fields in Kantowski-Sachs and Bianchi type III Lorentzian manifolds

TL;DR

This paper classifies proper homothetic vector fields in Kantowski-Sachs and Bianchi type III Lorentzian manifolds, revealing that certain classes admit five-dimensional homothetic symmetry groups.

Contribution

It provides a complete classification of proper homothetic vector fields in these space-times using direct integration, identifying cases with five-dimensional symmetry groups.

Findings

Certain classes admit proper homothetic vector fields

The dimension of these vector fields is five

The classification is achieved via direct integration technique

Abstract

A complete study of Kantowski-Sachs and Bianchi type III space-times according to their proper homothetic vector fields is given by using direct integration technique. Using the above mentioned technique we have shown that very special classes of the above space-times admit proper homothetic vector fields. The dimension of homothetic vector fields is five.