Homotheties and topology of tangent sphere bundles

Abstract

We prove a Theorem on homotheties between two given tangent sphere bundles $S_{r}M$ of a Riemannian manifold $M,g$ of $\dim \ge 3$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced by the conformal class of $g$. New examples are shown of manifolds with constant positive or with constant negative scalar curvature, which are not Einstein. Recalling results on the associated almost complex structure $I^G$ and symplectic structure ${\omega }^G$ on the manifold $TM$, generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds $TM$ and $S_{r}M$.

15 pages, to appear in Journal of Geometry

References in corpus (4)

• The Srni lectures on non-integrable geometries with torsion
• Weighted metrics on tangent sphere bundles
• On the characteristic connection of gwistor space
• Curvatures of weighted metrics on tangent sphere bundles

Cited by in corpus (8)

• On vector bundle manifolds with spherically symmetric metrics
• Weighted metrics on tangent sphere bundles
• A fundamental differential system of Riemannian geometry
• Notes on the Sasaki metric
• A fundamental differential system of 3-dimensional Riemannian geometry
• The ciconia metric on the tangent bundle of an almost-Hermitian manifold
• On the characteristic connection of gwistor space
• An invariant Kähler metric on the tangent disk bundle of a space-form