Harmonic morphisms of compact homogeneous spaces of positive curvature

Abstract

In this paper, we show that the projection of every compact Riemannian manifold of positive curvature onto a rank one symmetric space is harmonic. As a corollary, an infinite family of distinct harmonic morphisms with minimal circle fibers from the 7-dimensional homogeneous Aloff-Wallach spaces of positive curvature onto the 6-dimensional flag manifolds is given.