| In 1983, Futaki introduced the Futaki invariant, which is an obstruction to existence of a Kahler-Einstein metric on compact complex manifolds with positive first Chern class. Around the same time, Bando generalized this idea and introduced the Bando-Futaki invariants, which are obstructions to the harmonicity of the higher order Chern forms on compact complex manifolds with positive Chern class. In my dissertation, the Bando-Futaki Invariants on hypersurfaces are given as constants depending on the degree of the defining polynomials, the dimension of the underlying projective space, and the given holomorphic vector field. In addition, the holomorphic invariant introduced by Tian and Chen (Ricci Flow on Kahler-Einstein surfaces) is proven to be the Futaki invariant on connected Kahler manifolds. An improved version of Tian-Yau-Zelditch asymptotic expansions is given. |
