Abbassi, M. T. K.; Calvaruso, G. The curvature tensor of \(g\)-natural metrics on unit tangent sphere bundles. (English) Zbl 1148.53018 Int. J. Contemp. Math. Sci. 3, No. 5-8, 245-258 (2008). Let \(T_1M\) denote the unit tangent sphere bundle of a Riemannian manifold. The authors compute the curvature tensor corresponding to a metric on \(T_1M\) induced by a Riemannian g-natural metric on \(TM\) (either the Sasaki metric or the Cheeger-Gromoll metric). To this end, making use of the Gauss equation, the authors show a relation between the curvature tensor on \(T_1M\) and the tangential component of the curvature tensor of \(TM\). This relation involves also the shape operator of \(T_1M\) in \(TM\) and the second fundamental form. Reviewer: Gabriela Paola Ovando (Santa FĂ©) Cited in 10 Documents MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53D10 Contact manifolds (general theory) Keywords:unit tangent sphere bundle; \(g\)-natural metric; curvature tensor PDFBibTeX XMLCite \textit{M. T. K. Abbassi} and \textit{G. Calvaruso}, Int. J. Contemp. Math. Sci. 3, No. 5--8, 245--258 (2008; Zbl 1148.53018)