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.
An exotic T_1 S^4 with positive curvature / L. Verdiani; K. Grove; W. Ziller. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - STAMPA. - 21:(2011), pp. 499-524.
An exotic T_1 S^4 with positive curvature
VERDIANI, LUIGI;
2011
Abstract
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.File in questo prodotto:
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