Abstract
We prove a new rigidity result for an open manifold with nonnegative sectional curvature whose soul is odd-dimensional. Specifically, there exists a geodesic in and a parallel vertical plane field along it with constant vertical curvature and vanishing normal curvature. Under the added assumption that the Sharafutdinov fibers are rotationally symmetric, this implies that for small , the distance sphere contains an immersed flat cylinder, and thus could not have positive curvature.
Citation
Kristopher Tapp. "Rigidity for odd-dimensional souls." Geom. Topol. 16 (2) 957 - 962, 2012. https://doi.org/10.2140/gt.2012.16.957
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