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3+1 decompositions of differential forms on a Lorentzian manifold (M,g;+ - --) with respect to arbitrary observer field and the decomposition of thestandard operations acting on them are studied, making use of the ideas of thetheory of connections on principal bundles. Simple explicit general formulasare given as well as their application to the Maxwell equations.Comment: 15 pages, AmsTeX, to be published in J.Math.Phys. (sept.'97), minor  changes don

On 3+1 decompositions with respect to an observer field via differential forms