Fatness and positive curvatures on Riemannian submersions
Guided by rather counterintuitive properties of \emph{dual holonomy fields}, we introduce different notions of \emph{fatness} for Riemannian submersions. We introduce \emph{integral fatness} as an intrinsic condition implied by positive sectional curvature; \emph{sub-fatness} as a rigidity constraint that naturally ari...