The Scalar Curvature of the Tangent Bundle with Special Almost Product Metric

We study a class of Riemannian metrics $\widetilde g$ on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$ which contains, in particular, the Sasaki and the Cheeger–Gromoll metrics. In the case when $(M,g)$ is a space of constant section curvature $k$, we find conditions under which the scalar curvature $\widetilde S$ of $(TM,\widetilde g)$ is constant.