On Almost Paracontact Almost Paracomplex Riemannian Manifolds
Abstract
Almost paracontact manifolds of odd dimension having an almost paracomplex structure on the paracontact distribution are studied. The components of the
fundamental (0,3)-tensor, derived by the covariant derivative of the structure endomorphism and the metric on the considered manifolds in each of the basic classes, are obtained. Then, the case of the lowest dimension 3 of these manifolds is considered. An associated tensor of the Nijenhuis tensor is introduced and the studied manifolds are characterized with respect to this pair of tensors. Moreover, a cases of paracontact and para-Sasakian types are commented. A family of examples is given.
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