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Odd-dimensional Weyl and pseudo-Weyl spaces admitting almost contact, almost paracontact and nilpotent structures are considered in this work. The results are obtained by means of the apparatus of the prolonged covariant differentiation. A linear connection with torsion is constructed. With respect to this connection the prolonged covariant derivatives of the fundamental tensors of the Weyl and pseudo-Weyl spaces are found to be zero. The curvature tensor with respect to this connection is considered. MSC(2010): 53B05, 53B99. Keywords: composition, almost contact structure, almost paracontact structure, nilpotent structure, Weyl space, prolonged differentiation.

Odd-dimensional Weyl and pseudo-Weyl spaces with additional tensor structures