Enveloppe inférieure de fonctions admissibles sur la Grassmannienne G2,4C en présence de symétries

In a preceding work (Ben Abdesselem, 2006 [3]), the first author proves the existence of a lower bound of all admissible functions with sup equal to zero on some toric algebraic manifolds. The considered functions are invariant under the action of automorphisms group, obtained from the one on Pm(C). We prove an analogous result on the Grassmannian G2,4C by considering an automorphisms group. This gives, a new method for computing Tian constant (Tian, 1987 [8]) (see also Aubin, 1984 [1]) relative to this class of functions in a non toric case.