A note on quasi-positive curvature conditions

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 HPn for each n⩾2, and a family of finite quotients of T1S6.