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The curvature of the Sasaki metric of tangent sphere bundles
Authors:A L Yampol'skií
Abstract:We study the sectional curvaturesK of the Sasaki metric of tangent sphere bundles over spaces of constant curvatureK(T 1(M n, K)). We give precise bounds on the variation of the Ricci curvature and a bound on the scalar curvature ofT 1 (M n, K) that is uniform onK. In an appendix we calculate and give lower bounds for the lengths of closed geodesics onT 1 S n. titles.Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 132–145.
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