Homotheties and topology of tangent sphere bundles

Details Homotheties and topology of tangent sphere bundles Homotheties and topology of tangent sphere bundles

2010-12-19

arxiv.org/abs/1012.4135v1

Mathematics

Differential Geometry

15 pages

Scientific paper

We prove a Theorem on homotheties between two given tangent sphere bundles $S_rM$ of a Riemannian manifold $M,g$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced just by the conformal class of $g$. We show the associated almost complex and symplectic structures on the manifold $TM$, generalizing the well known structure of Sasaki. Finally the characteristic classes of Chern and Stiefel-Whitney are computed for the manifolds $TM$ and $S_rM$.

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