Weighted metrics on tangent sphere bundles

Abstract

Natural metric structures on the tangent bundle and tangent sphere bundles $S_{r}M$ of a Riemannian manifold $M$ with radius function $r$ enclose many important unsolved problems. Admitting metric connections on $M$ with torsion, we deduce the equations of induced metric connections on those bundles. Then the equations of reducibility of $TM$ to the almost Hermitian category. Our purpose is the study of the natural contact structure on $S_{r}M$ and the $G_2$-twistor space of any oriented Riemannian 4-manifold.

Accepted and about to appear in Quarterly Journal of Mathematics. 16 pages. This was the final draft submitted, before print proofs

References in corpus (2)

• The Srni lectures on non-integrable geometries with torsion
• Homotheties and topology of tangent sphere bundles

Cited by in corpus (5)

• Homotheties and topology of tangent sphere bundles
• On vector bundle manifolds with spherically symmetric metrics
• A fundamental differential system of Riemannian geometry
• A fundamental differential system of 3-dimensional Riemannian geometry
• An invariant Kähler metric on the tangent disk bundle of a space-form