2004/11/29 by Valery Marenich, Marenich, Valery
Mathematics · #53C20 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20 #msc:53C21
paper · pdf · doi:10.48550/arxiv.math/0411632
21 pages
arxiv created 2004/11/29 · arxiv updated 2009/12/01
As the first step in the direction of the Hopf conjecture on the non-existence of metrics with positive sectional curvature on S2 × S2 D.Gromoll and K.Tapp in [GT] suggested the following (Weak Hopf) conjecture (on the rigidity of non-negatively curved metrics on S2 × R3): "The boundary S2× S2 of the S2 × B3⊂ S2 × R3 with an arbitrary complete metric of non-negative sectional curvature contains a point where a curvature of S2 × S2 vanish". In this note we verify this.