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arXiv · 2308.09173

On quaternionic bisectional curvature

Oscar Macia·Uwe Semmelmann·Gregor Weingart
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Abstract

In this article we study the concept of quaternionic bisectional curvature introduced by B. Chow and D. Yang for quaternion-K\"ahler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space. We also show that all symmetric quaternion-K\"ahler manifolds different from the quaternionic projective space admit quaternionic lines of negative quaternionic bisectional curvature. In particular this implies that non-negative sectional curvature does not imply non-negative quaternionic bisectional curvature. Moreover we give a new and rather short proof of a classification result by A. Gray on compact K\"ahler manifolds of non-negative sectional curvature.

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Oscar Macia, Uwe Semmelmann, Gregor Weingart. 2023-08-17. On quaternionic bisectional curvature. https://arxiv.org/abs/2308.09173

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