Paracontact Tangent Bundles with Cheeger–Gromoll Metric

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 R and the sectional curvature K of the almost paracontact C–G metric tangent bundle TM. Finally, we obtain the Ricci curvature S 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.