Abstract
This paper deals with properties of the Cheeger-Gromoll metric $\overline{g}$ introduced in 1988 by Musso and Tricerri on the tangent bundle $TM$ associated to a given Riemannian metric $(M, g)$. One can find here essentially the two following results: 1. A classification of Killing vector fields on $(TM,\overline{g})$. 2. A generalization of a result of M. Sekizawa concerning the non rigidity of the Cheeger-Gromoll metric.
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