2014/12/02 by Jianquan Ge, Ge, Jianquan, Zizhou Tang +1
Mathematics · #53C20 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:53C20 #msc:53C30
paper · pdf · doi:10.48550/arxiv.1412.0982
This paper has been withdrawn by the authors. As pointed out to us by Chao Qian, Martin Kerin and Burkhard Wilking, Theorem 3.1 is incorrect, namely, the zero locus should be larger than that in Theorem 3.1. We are sincerely grateful to them for their valuable comments. Nevertheless, the metrics we constructed have positive sectional curvature almost everywhere on the Gromoll-Meyer sphere and on the homotopy (not diffeomorphic) RP^7
openalex publication_date 2014/12/02 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A metric with positive sectional curvature on the Gromoll-Meyer exotic 7-sphere is constructed explicitly. The proof relies on a 2-parameter family of left invariant metrics on Sp(2) and a one-parameter family of conformal deformations via an isoparametric function F on it. One byproduct is a metric with positive sectional curvature on a homotopy (but not diffeomorphic) RP7.