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Mathematische Annalen

, Volume 332, Issue 1, pp 81–101 | Cite as

Homeomorphism classification of positively curved manifolds with almost maximal symmetry rank

  • Fuquan FangEmail author
  • Xiaochun Rong
Article

Abstract.

We 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≥5) of positive sectional curvature on which an (m−1)-torus acts isometrically is homeomorphic to a complex projective space if and only if its Euler characteristic is not 2. By [Wi], these results imply a homeomorphism classification for positively curved n-manifolds (n≥8) of almost maximal symmetry rank Open image in new window

Keywords

Manifold Curve Manifold Maximal Symmetry Symmetry Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Nankai Institute of MathematicsNankai UniversityTianjingP.R. China
  2. 2.Mathematics DepartmentRutgers UniversityNew BrunswickUSA
  3. 3.Mathematics DepartmentCapital Normal UniversityBeijingP.R. China
  4. 4.Mathematics DepartmentCapital Normal UniversityBeijingP.R. China

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