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On Quaternionic Bisectional Curvature by Macia, Oscar; Semmelmann, Uwe; Weingart, Gregor is a scholarly article available to read on EtoBox.

What is On Quaternionic Bisectional Curvature about?

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.

Author

Macia, Oscar; Semmelmann, Uwe; Weingart, Gregor

Published

2023

Language

EN