Homeomorphism Classification of positively curved manifolds with almost maximal symmetry rank

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dc.creatorFang, Fuquan
dc.creatorRong, Xiaochun
dc.date2003-11-12
dc.date.accessioned2026-07-07T05:02:48Z
dc.date.available2026-07-07T05:02:48Z
dc.descriptionWe show that a closed simply connected 8-manifold (9-manifold) of positive sectional curvature on which a 3-torus (4-torus) acts isometrically is homeomorphic to a sphere, a complex projective space or a quaternionic projective plane (sphere). We show that a closed simply connected 2m-manifold (m>4) of positive sectional curvature on which a (m-1)-torus acts isometrically is homeomorphic to a complex projective space if and only if its Euler characteristic is not 2. By a result of Wilking, these results imply a homeomorphism classification for positively curved n-manifolds (n>7) of almost maximal symmetry rank [\frac{n-1}2].
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0311183
dc.identifierhttp://arxiv.org/abs/math/0311183
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69157
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53C20,53C23
dc.titleHomeomorphism Classification of positively curved manifolds with almost maximal symmetry rank
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