2010/05/12 by Rui Albuquerque, Albuquerque, Rui
Mathematics · Physics and Astronomy · #53C05 #53C07 #53C15 #53C17 #53C25 #53C28 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C05 #msc:53C07 #msc:53C15 #msc:53C17 #msc:53C25 #msc:53C28
paper · pdf · doi:10.48550/arxiv.1005.2150
This paper has been withdrawn by the author due to an error in equation 90. The final conclusions are therefore not true
openalex publication_date 2010/05/12 · arxiv created 2010/06/01 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Natural metric structures on tangent bundles and tangent sphere bundles enclose many important problems, from the topology of the base to the determination of their holonomy. We make here a brief study of the topic. We find the characteristic classes of some of those structures. We solve the question of when two given tangent sphere bundles SrM of a Riemannian manifold M,g are homothetic, assuming different variable radius functions r and weighted metrics induced only by the conformal class of g. We determine their Riemannian, Ricci, scalar and mean curvatures in some cases. We find a family of positive scalar curvature metrics on SrM when M has positive scalar curvature or when it has bounded sectional curvature and index of nullity 0. Our objective is the study of contact structures and gwistor spaces, a recently found natural G2-structure on S1M.