Some theorems on locally Riemannian spaces

]) , we have generalized the notion of analytic tensors and obtained the one of -tensors. As a natural developement, we shall deal with locally product Riemannian spaces. Since such a space is formally analogous to a Kahlerian space, it seems to be interesting to translate well known theorems in the latter to the former. We shall devote 1 to preliminaries. In 2, we shall obtain an integral formula for a tensor field in a compact orientable space and give an application on harmonic tensors. In 3 another application will be given and we shall see that in a compact orientable locally product Riemannian space an infinitesimal projective (or conformal) transformation is necessarily an isometry. In 6 we shall discuss infinitesimal product-projective transformations which correspond to holomorphically projective transformations in a Kahlerian space. Its preliminary results are given in 4 and 5. In 7 infinitesimal product-conformal transformations are defined and discussed.