Homotheties and topology of tangent sphere bundles
Rui Albuquerque

TL;DR
This paper explores the geometry and topology of tangent sphere bundles over Riemannian manifolds, providing new examples of manifolds with constant scalar curvature that are not Einstein, and analyzing associated complex and symplectic structures.
Contribution
It introduces homothety results for tangent sphere bundles with variable radii and weighted Sasaki metrics, and computes characteristic classes for these structures.
Findings
New examples of manifolds with constant scalar curvature that are not Einstein
Homothety theorems for tangent sphere bundles with variable radii
Calculations of Chern and Stiefel-Whitney classes for tangent bundles
Abstract
We prove a Theorem on homotheties between two given tangent sphere bundles of a Riemannian manifold of , assuming different variable radius functions and weighted Sasaki metrics induced by the conformal class of . 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 and symplectic structure on the manifold , 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 and .
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