Geodesic
The Scalar Curvature of the Tangent Bundle with Special Almost Product Metric
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 178-182

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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.
Keywords: almost product structure, tangent bundle, Riemannian metric, sectional curvature, scalar curvature. 
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     author = {O. V. Sukhova},
     title = {The {Scalar} {Curvature} of the {Tangent} {Bundle} with {Special} {Almost} {Product} {Metric}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {178--182},
     publisher = {mathdoc},
     volume = {151},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a14/}
}
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O. V. Sukhova. The Scalar Curvature of the Tangent Bundle with Special Almost Product Metric. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 4, pp. 178-182. http://geodesic.mathdoc.fr/item/UZKU_2009_151_4_a14/