most citedHomeomorphism Classification of positively curved manifolds with almost maximal symmetry rank

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Homeomorphism Classification of positively curved manifolds with almost maximal symmetry rank

Fuquan Fang, Xiaochun Rong

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 comple…

math.DG2003

Positively curved manifolds with maximal discrete symmetry rank

Fuquan Fang, Xiaochun Rong

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 act…

math.DG2003

Collapsed Riemannian manifolds with bounded sectional curvature

Xiaochun Rong

In the last two decades, one of the most important developments in Riemannian geometry is the collapsing theory of Cheeger-Fukaya-Gromov. A Riemannian manifold is called (sufficien…