Abstract
The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A \({\mathcal{D}}\) -homothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is proved that their scalar curvature is a constant, and it is shown that in the paraSasakian case these spaces can be obtained from Einstein paraSasakian manifolds with \({\mathcal{D}}\) -homothetic transformations. It is shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the paracontact structure is skew-symmetric and the defining vector field is Killing.
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Zamkovoy, S. Canonical connections on paracontact manifolds. Ann Glob Anal Geom 36, 37–60 (2009). https://doi.org/10.1007/s10455-008-9147-3
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DOI: https://doi.org/10.1007/s10455-008-9147-3
Keywords
- ParaSasakian manifolds
- Paracontact manifolds
- \({\mathcal{D}}\) -homothetic transformations
- Gauge transformations
- Connection with totally skew-symmetric torsion