2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90737We consider the manifold-valued, stochastic extension of the Schrödinger equation introduced by Hughston (Proc.Roy.Soc.Lond. A452 (1996) 953) in a manifestly covariant, differential-geometric framework, and examine the resulting quantum evolution on some specific examples of Kähler manifolds with many symmetries. We find conditions on the curvature for the evolution to be a `collapse process' in the sense of Brody and Hughston (Proc.Roy.Soc.Lond. A458 (2002) 1117) or, more generally, a `reduction process', and give examples that satisfy these conditions. For some of these examples, we show that the Lüders projection postulate admits a consistent interpretation and remains valid in the nonlinear regime.latex, 23 pagesQuantum PhysicsGeneral Relativity and Quantum Cosmologytext