Abstract
In this paper, we define the almost paracontact metric structure on a tangent bundle TM with Cheeger–Gromoll (C–G) metric and obtain the normality condition for it. We define the paracontact C–G metric tangent bundle, K-paracontact C–G metric tangent bundle and C–G para-Sasakian tangent bundle and give some characterizations about them. Also, we give the Riemannian curvature tensor R̃ and the sectional curvature K̃ of the almost paracontact C–G metric tangent bundle TM. Finally, we obtain the Ricci curvature S̃ and the scalar curvature \({\tilde{\sigma}}\) of the almost paracontact C–G metric tangent bundle TM with the aid of the orthonormal basis of TM.
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Kazan, A., Karadağ, H.B. Paracontact Tangent Bundles with Cheeger–Gromoll Metric. Mediterr. J. Math. 12, 497–523 (2015). https://doi.org/10.1007/s00009-014-0414-1
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DOI: https://doi.org/10.1007/s00009-014-0414-1