Homeomorphism classification of positively curved manifolds with almost maximal symmetry rank

By F. Fang, Xiaochun Rong. 2003

53 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c92828f5f93820261855011d04b3cc6c01932e6a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Torus actions on manifolds of positive sectional curvature (2003, background): “This actually has been answered by Rong [21].”