  We prove a generalization of the second variation formula of the Robin
function associated to a smooth variation of domains in C^N to the case of the
c-Robin function associated to a smooth variation of domains in a complex
manifold M equipped with a Hermitian metric and a smooth, nonnegative function
c. Our purpose is that, with this added flexibility, we are able to give a
criterion for a bounded, smoothly bounded, pseudoconvex domain D in a complex
homogeneous space to be Stein.
