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The purpose of this work is to prove a generalization of the multiplicative index of a product manifold in the case of a fiber manifold in which the fundamental group of the base space acts trivialiy on the cohomoly sing of the fiber. In Chapters ] and 2 we introduce the basic tools: Leary-Serre Theorem, Index of a manifold, index of a Poincaré ring and its algebraic properties- In Chapter 3 we characterize the spectral sequence of the Leary- -Serre Theorem and prove the main theorem of this work. In Chapter à, we present an application.