2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73880The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and existence results in two different frameworks, using differential geometry tools. Applications to PDEs are given, including a certain class of Dirichlet problems on manifolds.47 pages To be published in PTRFProbabilityMSC (2000) 58J65 34F05 60G48text