2014/11/30 by Rui Albuquerque, R. Albuquerque
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Bundle #Differential geometry #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holonomy #Levi-Civita connection #Manifold (fluid mechanics) #Metric (unit) #Normal bundle #Tangent bundle #Tangent space #Unit tangent bundle #Vector bundle #math.DG #msc:53C07 #msc:53C22 #msc:53C25 #msc:53C29 #msc:53C55
paper · pdf · doi:10.1007/s10455-016-9528-y
published as Ann Glob Anal Geom (2017) 51:129-154 · Final version
openalex created_date 2016/06/24 · openalex publication_date 2016/09/26 · arxiv created 2017/02/26 · arxiv updated 2017/02/28 · openalex updated_date 2026/08/05
We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle E→ M, over a Riemannian manifold M, when E is endowed with a metric connection. The tangent bundle of E admits a canonical decomposition and thus it is possible to define an interesting class of two-weights metrics with the weight functions depending on the fibre norm of E; hence the generalized concept of spherically symmetric metrics. We study its main properties and curvature equations. Finally we focus on a few applications and compute the holonomy of Bryant-Salamon type G2 manifolds.