Non-fiber preserving actions on prism manifolds

Abstract

In this paper we classify the finite groups of isometries which act on a prism manifolds M(b,d) and do not preserve any fibering. We construct nine distinct finite groups of isometries which act on M(1,2), and do not preserve any fibering. We then show that if a finite group of isometries G acts on M(b,d) and does not preserve any fibering, then M(b,d) = M(1,2) and G is conjugate to one of these nine groups which are: Z₃ × T, T, O, S₃ × O, Z₃ ∘ O, S₃ × T, Z₃ × O, Z₃ × I, and S₃ × I , where T, O, I and S₃ are the tetrahedral, octahedral, icosahedral, and symmetric groups respectively.