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arXiv · 1201.1312

A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds

Fernando Galaz-Garcia
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Abstract

We show that any effective isometric torus action of maximal rank on a compact Riemannian manifold with positive (sectional) curvature and maximal symmetry rank, that is, on a positively curved sphere, lens space, complex or real projective space, is equivariantaly diffeomorphic to a linear action. We show that a compact, simply connected Riemannian 4- or 5-manifold of quasipositive curvature and maximal symmetry rank must be diffeomorphic to the 4-sphere, complex projective plane or the 5-sphere.

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Fernando Galaz-Garcia. 2012-01-05. A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds. https://arxiv.org/abs/1201.1312

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