Geometrically formal homogeneous metrics of positive curvature

Manuel Amann; Wolfgang Ziller

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arXiv · 1407.6201

Geometrically formal homogeneous metrics of positive curvature

Manuel Amann·Wolfgang Ziller

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Abstract

A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold admitting a Riemannian metric of positive sectional curvature is conjectured to be topologically formal. Nonetheless, we show that among the homogeneous Riemannian metrics of positive sectional curvature a geometrically formal metric is either symmetric, or a metric on a rational homology sphere.

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Manuel Amann, Wolfgang Ziller. 2014-07-23. Geometrically formal homogeneous metrics of positive curvature. https://arxiv.org/abs/1407.6201

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