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

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dc.creatorReznikov, Alexander
dc.date1994-10-16
dc.date.accessioned2026-07-07T09:12:26Z
dc.date.available2026-07-07T09:12:26Z
dc.descriptionWe 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.
dc.description6 pages, plane TEX
dc.identifierhttps://arxiv.org/abs/dg-ga/9410006
dc.identifierhttp://arxiv.org/abs/dg-ga/9410006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152019
dc.subjectDifferential Geometry
dc.titleGeometry of Cyclic Quotients, I: Knotted Totally Geodesic Submanifolds in Positively Curved Spheres
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