A coincidence theorem for holomorphic maps to G/P

The purpose of this note is to extend to an arbitrary generalized Hopf and CalabiEckmann manifold the following result of Kalyan Mukherjea: Let Vn = S 2n+1×S2n+1 denote a Calabi-Eckmann manifold. If f, g : Vn−→P are any two holomorphic maps, at least one of them being non-constant, then there exists a coincidence: f(x) = g(x) for some x ∈ Vn. Our proof involves a coincidence theorem for holomorphic maps to complex projective varieties of the form G/P where G is complex simple algebraic group and P ⊂ G is a maximal parabolic subgroup, where one of the maps is dominant.