  In this paper, the projective geometry is used to describe the features of
spherical manifold and discreteness in quantum evolution. As a system evolves
in time the state vector changes and it traces out a curve in Hilbert space.
Geometrically, the evolution is represented as a closed curve in the projective
Hilbert space. In recent times many attempts have been made to describe
'length', 'distance', and 'geometric phases' and also 'parallel transport'and
symplectic geometry in various ways in the projective Hilbert space, during
quantum evolution. It is shown in this paper that for the quantum evolution in
ray space, spherical manifold and features of discreteness can be described
geometrically.
