Pair of associated Schouten-van Kampen connections adapted to an almost paracontact almost paracomplex Riemannian structure

TL;DR

This paper introduces and analyzes a pair of specialized affine connections on manifolds with almost paracontact almost paracomplex Riemannian structures, characterizing their properties and providing explicit examples.

Contribution

It develops a new pair of associated Schouten-van Kampen connections adapted to these structures and explores their curvature and classification properties.

Findings

Characterization of basic classes of manifolds with the structure

Curvature properties of the constructed connections

Explicit examples on a Lie group

Abstract

There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the paracontact distribution and an almost paracontact almost paracomplex Riemannian structure generated by the pair of associated metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic classes of the manifolds with the considered structure are characterized. Curvature properties of the studied connections are obtained. A family of examples on a Lie group is constructed.