In this thesis solutions have been found for Kahler equation in spinorial form on spacetime with constant curvature by using Fermi normal coordinates. Expressing Kahler equation in spinorial form demands investigation of Clifford algebra with perturbed generators and calculation of the gravitational terms. The results indicate that there are four types of spinor fields reflecting the existence of four types of each 1/2-spin particle. Also there is an indication about the relationships between the state of the particle and the energy of interactions with gravitational field for a freely falling particle. The form of Kahler equation in the presence of Coulomb field in curved space-time was found. Obtaining this form represents the first step in finding-a solution for Kahler ' equation for hydrogen like atoms.