2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184589We study gauge theories based on abelian $p-$forms on real compact hyperbolic manifolds. An explicit formula for the conformal anomaly corresponding to skew--symmetric tensor fields is obtained, by using zeta--function regularization and the trace tensor kernel formula. Explicit exact and numerical values of the anomaly for $p-$forms of order up to $p=4$ in spaces of dimension up to $n=10$ are then calculated.13 pages, 2 tablesMathematical PhysicsFunctional Analysis81T50, 14D21,58A10text