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Prolongations of Riemannian metrics from differentiable manifold to its linear frame bundle. (English. Russian original) Zbl 0776.53028
Russ. Math. 36, No. 6, 87-95 (1992); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1992, No. 6(361), 93-102 (1992).
The author deduces that the so-called complete lift \(g^ C\) of a Riemannian metric \(g\) on a manifold \(M\) to the bundle of all linear frames on \(M\) is a Riemannian metric as well. Then he studies the infinitesimal isometries of \(g^ C\) in connection with the infinitesimal isometries of \(g\).
Reviewer: I.Kolář (Brno)

MSC:
53C20 Global Riemannian geometry, including pinching
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