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A note on maximal symmetry rank, quasipositive curvature, and low dimensional manifolds. [Preprint]

Galaz-Garcia, Fernando

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.

Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Buchaufsatz
Jahr 2013
Sprache Englisch
Identifikator KITopen ID: 1000051161
Erschienen in arXiv [math.DG]
Seiten arXiv:1201.1312
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