A Coincidence Theorem for Holomorphic Maps to G/P

The purpose of this note is to extend to an arbitrary generalized Hopf and Calabi-Eckmann manifold the following result of Kalyan Mukherjea: Let Vn = S^(2n+1) x S^(2n+1) denote a Calabi-Eckmann manifold. If f,g : Vn longrightarrow P^n 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 in 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 subset G is a maximal parabolic subgroup, where one of the maps is dominant.