Narrow Results

In this paper, we start the program of the existence of the smooth equivariant geodesics in the equivariant Mabuchi moduli space of Kähler metrics on type II cohomogeneity one compact Kähler manifold. In this paper, we deal with the manifolds $M_n$ obtained by blowing up the diagonal of the product of two copies of a $C{P}^n$.