Lobachevsky geometry of (super)conformal mechanics

Understand

We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system.

• Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane).
• We also extend this picture to the N=2k superconformal mechanics described in terms of Lobachevsky superspace.