Quantum Equivalence of Massive Antisymmetric Tensor Field Models in Curved Space

We study the effective actions for massive rank-2 and rank-3 antisymmetric tensor field models in curved space-time. These models are classically equivalent to massive vector field and massive scalar field with minimal coupling to gravity respectively. We prove that effective action for massive rank-2 antisymmetric tensor field is exactly equal to one for massive vector field and effective action for massive rank-3 antisymmetric tensor field is exactly equal to one for massive scalar field. Prove is based on an identity for mass-dependent zeta-functions associated with Laplacians acting on $p$-forms.