Metrics with nonnegative curvature on {S^2 \times \mathbb{R}^4} |
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Authors: | Kristopher Tapp |
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Institution: | 1. Department of Mathematics, Saint Joseph??s University, 5600 City Avenue, Philadelphia, PA, 19131, USA
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Abstract: | We study nonnegatively curved metrics on
S2×\mathbbR4{S^2\times\mathbb{R}^4}. First, we prove rigidity theorems for connection metrics; for example, the holonomy group of the normal bundle of the soul
must lie in a maximal torus of SO(4). Next, we prove that Wilking’s almost-positively curved metric on S
2 × S
3 extends to a nonnegatively curved metric on
S2×\mathbbR4{S^2\times\mathbb{R}^4} (so that Wilking’s space becomes the distance sphere of radius 1 about the soul). We describe in detail the geometry of this
extended metric. |
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Keywords: | |
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