Obstructions to positive curvature and symmetry

Anand Dessai

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Obstructions to positive curvature and symmetry

Anand Dessai

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Abstract

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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BibTeX RIS

Anand Dessai. 2002-04-29. Obstructions to positive curvature and symmetry. https://arxiv.org/abs/math/0104256

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