  Focus of this study is to explore some aspects of mathematical foundations
for using complex manifolds as a model for space-time. More specifically,
certain equations of motions have been derived as a Projective geodesic on a
real manifold embedded within a complex one. To that goal, first the geodesic
on complex manifold has been computed using local complex and conjugate
coordinates, and then its projection on the real sub-manifold has been studied.
The projective geodesic, thus obtained, is shown to have additional terms
beyond the usual Christoffel symbols, and hence expands the geodesic to capture
effects beyond the mere gravitational ones.
