The geometry of the Sasaki metric on the sphere bundle of Euclidean Atiyah vector bundles

Mohamed Boucetta, Hasna Essoufi

Let $(M,⟨,{⟩}_{TM})$ be a Riemannian manifold. It is well-known that the Sasaki metric on $TM$ is very rigid but it has nice properties when restricted to $T^{(r)}M=\{u\i…