2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71967We review the recent results on the Jacobi field of a (real-valued) Lévy process defined on a Riemannian manifold. In the case where the Lévy process is neither Gaussian, nor Poisson, the corresponding Jacobi field acts in an extended Fock space. We also give a unitary equivalent representation of the Jacobi field in a usual Fock space. This representation is inspired by a result by Accardi, Franz, and Skeide (2002).ProbabilityFunctional Analysis60G51; 60G57; 60H40text