A note on teleparallel Killing vector fields in Bianchi type VIII and IX space–times in teleparallel theory of gravitation

In this paper we classify Bianchi type VIII and IX space—times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique. It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5. From the above study we have shown that the Killing vector fields for Bianchi type VIII and IX space—times in the context of teleparallel theory are different from that in general relativity.