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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.

DOI Code: 10.1285/i15900932v41n1p1

Keywords: Riemannian submersion; homogeneous space; Aloff-Wallach space; positive curvature; harmonic morphism

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