Vector field energies and critical metrics on Kähler manifolds (Q2731030)

Associated with a Hamiltonian holomorphic vector field on a compact Kähler manifold, a nice functional on the space of Kähler metrics is constructed. It is using the integration of the bilinear pairing (following classical ideas of A. Futaki and T. Mabuchi), contracted with the Hamiltonian holomorphic vector field. As application the author gets three new functionals whose critical points are extremal Kähler metrics or Kähler-Einstein metrics on the manifold. As a consequence uniqueness of Kähler-Einstein metrics on nonsingular toric Fano varieties, possibly with nonvanishing Futaki character, is proved.