Weighted metrics on tangent sphere bundles

Details Weighted metrics on tangent sphere bundles Weighted metrics on tangent sphere bundles

2010-12-19

arxiv.org/abs/1012.4139v1

Mathematics

Differential Geometry

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

Scientific paper

Natural metric structures on the tangent bundle and tangent sphere bundles $S_rM$ 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 $S_rM$ and the $G_2$-twistor space of any oriented Riemannian 4-manifold.

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