Positively curved manifolds with maximal discrete symmetry rank
| dc.creator | Fang, Fuquan | |
| dc.creator | Rong, Xiaochun | |
| dc.date | 2003-08-14 | |
| dc.date.accessioned | 2026-07-07T05:00:24Z | |
| dc.date.available | 2026-07-07T05:00:24Z | |
| dc.description | Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a constant p(n)>0 such that (1) If M^{2n} admits an effective isometric \Bbb Z_p^k-action for a prime p\ge p(n), then k\le n and ``='' implies that M^{2n} is homeomorphic to a sphere or a complex projective space. (2) If M^{2n+1} admits an isometric S^1 x \Bbb Z_p^k-action for a prime p\ge p(n), then k\le n and ``='' implies that M is homeomorphic to a sphere. (3) For M in (1) or (2), if n\ge 7 and k\ge [\frac{3n}4]+2, then M is homeomorphic to a sphere or homotopic to a complex projective space. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308139 | |
| dc.identifier | http://arxiv.org/abs/math/0308139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68314 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C20, 57R19 | |
| dc.title | Positively curved manifolds with maximal discrete symmetry rank | |
| dc.type | text |