Thu, Oct 24
1:00 PM — 2:00 PM
North Academic Center160 Convent AvenueNAC 6/113
North Academic Center, NA 6/113
Renato Bettiol (University of Notre Dame), Strong positive sectional curvatureCompact Riemannian manifolds with positive sectional curvature are very special objects that have been studied since the beginning of Riemannian geometry. Nevertheless, there are currently very few known examples and many conjectures regarding these objects remain elusive. A much stronger notion is that of manifolds with positive curvature operator, which have been completely classified through the use of Ricci flow. In this talk, I will describe an intermediate notion between the above two, that has not received much attention but essentially dates back to the work of Thorpe in the early 70's. The interest in this class arises from trying to understand the "gap" between the classes of manifolds with positive curvature operator and positive sectional curvature, with the hope to better understand the latter. This is joint work with R. Mendes (Notre Dame).