2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139715We 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.126 pages, 2 figuresComplex Variables32U10text