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In this paper we present a bundle of pairs of volume forms V2. We describe horizontal lift of a tensor of type (1; 1) and we show that horizontal lift of an almost complex structure on a manifold M is an almost complex structure on the bundle V2. Next we give conditions under which the almost complex structure on V 2 is integrable. In the second part we find horizontal lift of vector fields, tensorfields of type (0; 2) and (2; 0), Riemannian metrics and we determine a family of a t-connections on the bundle of pairs of volume forms. At the end, we consider some properties of the horizontally lifted vector fields and certain infinitesimal transformations.
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