A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds
Differential Geometry
2012-01-09 v1
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.
Keywords
Cite
@article{arxiv.1201.1312,
title = {A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds},
author = {Fernando Galaz-Garcia},
journal= {arXiv preprint arXiv:1201.1312},
year = {2012}
}