Positive curvature in dimension seven

Resumen:

I will detail a general construction for putting positive sectional curvature on a series of 7-manifolds discussed as viable candidates to carry positively curved metrics with co-dimension one principal orbits discussed by Grove, Wilking and Ziller in JDG in 2008 by appropriately modifying a naturally occurring 3-Sasakian metric. This builds on previous work where I considered isolated examples of this sort where the base Bianchi IX self-dual Einstein orbifold metric had an algebraic closed form.
 

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