An obstructions to Non-negative curvature on Bundles with Pull-back connections

2012/06/08 by Llohann Sperança, Sperança, Llohann
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.1206.1774

6 pages

arxiv created 2012/06/08 · arxiv updated 2012/06/11

Abstract

Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian submersions with totally geodesic fibers. In particular, we prove that the bundles in [5] and [1] have sections of negative curvature.

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