A note on proper affine symmetry in Kantowski-Sachs and Bianchi type III space-times
Ghulam Shabbir, Nisar Ahmed
TL;DR
This paper studies proper affine symmetries in Kantowski-Sachs and Bianchi type III space-times using holonomy, decomposability, Riemann matrix rank, and direct integration, identifying special classes with such symmetries.
Contribution
It identifies specific classes of Kantowski-Sachs and Bianchi type III space-times that admit proper affine vector fields using advanced geometric techniques.
Findings
Certain classes admit proper affine vector fields.
Proper affine symmetries depend on holonomy and decomposability.
The Riemann matrix rank influences symmetry properties.
Abstract
We investigate proper affine symmetry for the Kantowski-Sachs and Bianchi type III space-times by using holonomy and decomposability, the rank of the 6X6 Riemann matrix and direct integration techniques. It is shown that the very special classes of the above space-times admit proper affine vector fields.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Nonlinear Waves and Solitons · Black Holes and Theoretical Physics