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Two Lie Groups with Π-Structures That Exchange Their Membership in Two Basic Classes

by Mancho Manev, Veselina Tavkova, and Victoria Kuncheva

Posted: September 17, 2026
Server: Preprints.org
DOI: 10.20944/preprints202609.1494.v1

The investigation of almost paracontact almost paracomplex manifolds is further developed. These manifolds, referred to briefly as Π-manifolds, are equipped with a pair of mutually related compatible metrics: a Riemannian metric and a pseudo-Riemannian metric. Based on the established classification with respect to the Riemannian metric and the corresponding alternative classification with respect to the associated pseudo-Riemannian metric, two examples on a tree-dimensional Lie group are presented to illustrate the most significant case of the transition between the two classifications.

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