AN EXOTIC T1S4 WITH POSITIVE CURVATURE

作者：Grove Karsten^*; Verdiani Luigi; Ziller Wolfgang

来源：Geometric and Functional Analysis, 2011, 21(3): 499-524.

DOI：10.1007/s00039-011-0117-8

• Positive curvature
• connection metrics
• cohomogeneity one
• 3-Sasakian manifolds

We construct a metric with positive sectional curvature on a 7-manifold which supports an isometry group with orbits of codimension 1. It is a connection metric on the total space of an orbifold 3-sphere bundle over an orbifold 4-sphere. By a result of S. Goette, the manifold is homeomorphic but not diffeomorphic to the unit tangent bundle of the 4-sphere.

• 出版日期2011-6