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g -natural metrics of constant curvature on unit tangent sphere bundles

M. T. K. Abbassi, Giovanni Calvaruso (2012)

Archivum Mathematicum

We completely classify Riemannian g -natural metrics of constant sectional curvature on the unit tangent sphere bundle T 1 M of a Riemannian manifold ( M , g ) . Since the base manifold M turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian g -natural metric on the unit tangent sphere bundle of a Riemannian surface.

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