Geometric and Functional Analysis

, Volume 21, Issue 3, pp 499–524 | Cite as

An Exotic \({T_{1}\mathbb{S}^4}\) with Positive Curvature



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.

Keywords and phrases

Positive curvature connection metrics cohomogeneity one 3-Sasakian manifolds 

2010 Mathematics Subject Classification

Primary: 53C20 Secondary: 53C25 57S15 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Karsten Grove
    • 1
  • Luigi Verdiani
    • 2
  • Wolfgang Ziller
    • 3
  1. 1.Mathematics DepartmentUniversity of Notre DameNotre DameUSA
  2. 2.Dipartimento di Matematica ApplicataFirenzeItaly
  3. 3.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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