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 equivariantly 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. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
Galaz-Garcia, F. (2014). A note on maximal symmetry rank, Quasipositive curvature, and low dimensional manifolds. Lecture Notes in Mathematics, 2110, 45–55. https://doi.org/10.1007/978-3-319-06373-7_3
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