Coset for Hopf fibration and Squashing

Abstract

We provide a simple derivation of metrics for fundamental geometrical deformations such as Hopf fibration, squashing and Z_k quotient which play essential roles in recent studies on the AdS4/CFT3. A general metric formula of Hopf fibrations for complex and quaternion cosets is presented. Squashing is given by a similarity transformation which changes the metric preserving the isometry symmetry of the projective space. On the other hand Z_k quotient is given as a lens space which changes the topology preserving the "local" metric.