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Extrinsic geometry of the Gromoll-Meyer sphere
Differential Geometry and its Applications ( IF 0.6 ) Pub Date : 2020-04-27 , DOI: 10.1016/j.difgeo.2020.101638 Chao Qian , Zizhou Tang , Wenjiao Yan
中文翻译:
Gromoll-Meyer球的外在几何形状
更新日期:2020-04-27
Differential Geometry and its Applications ( IF 0.6 ) Pub Date : 2020-04-27 , DOI: 10.1016/j.difgeo.2020.101638 Chao Qian , Zizhou Tang , Wenjiao Yan
Among a family of 2-parameter left invariant metrics on , we determine which have nonnegative sectional curvatures and which are Einstein. On the quotient , we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to . Furthermore, on the quotient , we construct a transnormal system with transnormal hypersurfaces diffeomorphic to the Gromoll-Meyer sphere . Moreover, the induced metric on each hypersurface has positive Ricci curvature and quasi-positive sectional curvature simultaneously.
中文翻译:
Gromoll-Meyer球的外在几何形状
在2参数左不变指标族中 ,我们确定哪些具有非负截面曲率,哪些是爱因斯坦。关于商,我们构造了一个等参的等参叶面,其中等参超曲面对 。此外,关于商,我们构造了一个具有向Gromoll-Meyer球面变态的超正规超曲面的超正规系统 。此外,每个超表面上的诱导度量同时具有正Ricci曲率和准正截面曲率。