Metric of non-negative sectional curvature on the tangent bundle of the two-dimensional sphere (Q1083699)

Let \(S^ 2\) be the two-dimensional sphere and \(TS^ 2\) its tangent bundle. A metric of non-negative sectional curvature on \(TS^ 2\) is constructed and some properties of the corresponding curvature tensor field are established. Using previous considerations [the author, Sov. Math., Dokl. 24, 595-597 (1981); translation from Dokl. Akad. Nauk SSSR 261, 801-804 (1981; Zbl 0495.53037)], a complete proof of \textit{B. O'Neill}'s theorem [Mich. Math. J. 13, 459-469 (1966; Zbl 0145.186)], expressing the relation between the sectional curvatures of two Riemannian manifolds related by a Riemannian submersion, is also given.