Non-Compact Complex Projective Space as a Phase Space

Abstract

Abstract: First of all we give a simple example of Kähler manifolds (pseudo)Euclidean complex spaces as well as compact and non-compact complex projective spaces. Moreover we describe The Klein model of Lobachevsky space and mapping a conformal mechanics to itin one dimensional case first. Than we extend Klein model for the N-dimensional. We got interesting results that isometry generators of the phase space, namely Killing potentials are appear to be the constants of motion of the system.