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

Coset for Hopf fibration and Squashing