Orbifold fibrations of Eschenburg spaces |
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Authors: | Luis A Florit Wolfgang Ziller |
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Institution: | (1) IMPA, Est. Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil;(2) University of Pennsylvania, Philadelphia, PA 19104, USA |
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Abstract: | Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a
Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold
fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which
give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we
obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two
points.
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Keywords: | Positive curvature Orbifold fibrations Almost free circle actions |
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