Speaker: 欧阳泽轩博士后，西湖大学

Inviter: 简旺键副研究员

Title: Curvature Calculations for Metrics on the Gromoll–Meyer Sphere

Language: Chinese

Time & Venue: 2026.09.29 10:00-11:00 腾讯会议：574-8078-3311

Abstract: This talk focuses on the curvature calculations involved in the construction of a positively curved metric on the Gromoll–Meyer exotic 7-sphere. Starting from a family of deformed metrics on Sp(2), the sectional curvature of the induced quotient metric is analyzed through the geometry of horizontal two-planes. A central step is to characterize horizontal pairs whose leading curvature terms vanish and to reduce the remaining positivity problem to explicit algebraic expressions in the corresponding Lie algebra variables. Particular attention is given to the curvature expansion with respect to the deformation parameter, the identification of the relevant lower-order terms, and the treatment of the critical set where the first positive contribution degenerates. By establishing positivity of the first non-vanishing term and controlling the higher-order remainder uniformly, one obtains strict positivity of sectional curvature for sufficiently small deformation parameters.