On connections with torsion on nonholonomic para-Kenmotsu manifolds
- DOI
- 10.5922/0321-4796-2023-54-1-6
- Pages
- 49-63
Abstract
The concept of a nonholonomic para-Kenmotsu manifold is introduced. A nonholonomic para-Kenmotsu manifold is a natural generalization of a para-Kenmotsu manifold; the distribution of a nonholonomic para-Kenmotsu manifold does not need to be involutive. Properly nonholonomic para-Kenmotsu manifolds are singled out, these are nonholonomic para-Kenmotsu manifolds with non-involutive distribution. On an almost (para-)contact metric manifold, we introduce a metric connection with torsion, which is called a connection of Levi-Civita type in this paper. In the case of a nonholonomic para-Kenmotsu manifold, such a connection has a simpler structure than the Levi-Civita connection, and in some cases it turns out to be preferable from an applied point of view. A Levi-Civita type connection coincides with a Levi-Civita connection if and only if a nonholonomic para-Kenmotsu manifold reduces to a para-Kenmotsu manifold. It is proved that a proper nonholonomic para-Kenmotsu manifold cannot carry the structure of an Einstein manifold with respect to a connection of the Levi-Civita type.
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