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Geometry of Cyclic Quotients, I: Knotted Totally Geodesic Submanifolds in Positively Curved Spheres

Alexander Reznikov
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Abstract

We prove that there exists a metric of positive curvature in a three-sphere which admits a given torus knot as a closed geodesic.We also sketch a construction of a metric in a four sphere, very likely of positive curvature, which admits a totally geodesic projective plane with Euler number four. Surpisingly, the technique borrows a lot from the Mostow-Siu-Gromov-Thurston constuction of exotic negatively curved manifolds.

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BibTeXRIS

Alexander Reznikov. 1994-10-16. Geometry of Cyclic Quotients, I: Knotted Totally Geodesic Submanifolds in Positively Curved Spheres. https://arxiv.org/abs/dg-ga/9410006

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