2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33367In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds and prove that they are metric independent. In dimension four, the quaternionic analytic torsion equals to the self-dual analytic torsion. For higher dimensional manifolds, the self-dual analytic torsion is a conformal invariant.17 pages, LaTexDifferential Geometrytext