Bando-Futaki Invariants on Hypersurfaces

In this paper, the Bando-Futaki invariants on hypersurfaces are derived in terms of 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 K"ahler-Einstein surfaces) is proven to be the Futaki invariant on compact K"ahler manifolds with positive first Chern class.