Odd-Dimensional Weyl and Pseudo-Weyl spaces with Additional Tensor Structures

Abstract

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.