  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.
