Obstructions to positive curvature and symmetry

Details Obstructions to positive curvature and symmetry Obstructions to positive curvature and symmetry

2001-04-26

arxiv.org/abs/math/0104256v3

Mathematics

Differential Geometry

21 pages, revised version, new title

Scientific paper

We show that the indices of certain twisted Dirac operators vanish on a $Spin$-manifold $M$ of positive sectional curvature if the symmetry rank of $M$ is $\geq 2$ or if the symmetry rank is one and $M$ is two connected. We also give examples of simply connected manifolds of positive Ricci curvature which do not admit a metric of positive sectional curvature and positive symmetry rank.

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