A note on quasi-positive curvature conditions

Article history: Received 10 July 2013 Available online 17 April 2014 Communicated by D.V. Alekseevsky MSC: primary 53C21 secondary 53C20 We classify the triples H ⊂ K ⊂ G of nested compact Lie groups which satisfy the “positive triple” condition that was shown in [17] to ensure that G/H admits a metric with quasi-positive curvature. A few new examples of spaces that admit quasi-positively curved metrics emerge from this classification; namely, a CP2-bundle over S6, a B7-bundle over HP2, a CP2n−1-bundle over HP for each n 2, and a family of finite quotients of T 1S6. © 2014 Elsevier B.V. All rights reserved.