Gromoll-Meyer球的外禀几何
Extrinsic geometry of the Gromoll-Meyer sphere
摘要：
在Sp（2）上的一族2参数左不变度量中，我们确定了哪些度量具有非负截面曲率，哪些度量是Einstein度量.在广义$\widetilde{N}^{11}=(Sp(2)\times S^4)/S^3$上，我们构造了一个齐次等参叶理，它的等参超曲面与Sp（2）同构.进一步，在广义$\widetilde{N}^{11}/S^3$上，我们构造了一个超正规系统，其超正规超曲面与Gromoll-Meyer球面$Σ^7$同构.并且，每个超曲面上的诱导度量同时具有正的里奇曲率和拟正的截面曲率.
英文摘要：
Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $\widetilde{N}^{11}=(Sp(2)\times S^4)/S^3$, we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to Sp(2). Furthermore, on the quotiente $\widetilde{N}^{11}/S^3$, we construct a transnormal system with transnormal hypersurfaces diffeomorphic to the Gromoll-Meyer sphere $Σ^7$. Moreover, the induced metric on each hypersurface has positive Ricci curvature and quasi-positive sectional curvature simultaneously.
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