On quaternionic bisectional curvature

2023/08/17 by Macia, Oscar, Semmelmann, Uwe, Weingart, Gregor · 1 citation
#53C10 #53C15 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.09173

Abstract

In this article we study the concept of quaternionic bisectional curvature introduced by B. Chow and D. Yang for quaternion-Kähler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space. We also show that all symmetric quaternion-Kähler 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 Kähler manifolds of non-negative sectional curvature.

Cited by

• Hyperbolicity and Schwarz Lemmas in Calibrated Geometry

Related

• Quaternion-Kähler manifolds with non-negative quaternionic sectional curvature
• Quaternionic-Kähler manifolds with nonnegative sectional curvature
• Positive quaternionic Kaehler manifolds and symmetry rank
• Kähler C-spaces and quadratic bisectional curvature
• An example of compact Kähler manifold with nonnegative quadratic bisectional curvature