Abstract
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 quotient N˜11=(Sp(2)×S4)/S3, we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to Sp(2). Furthermore, on the quotient N˜11/S3, we construct a transnormal system with transnormal hypersurfaces diffeomorphic to the Gromoll-Meyer sphere Σ7. Moreover, the induced metric on each hypersurface has positive Ricci curvature and quasi-positive sectional curvature simultaneously.
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