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- Title
HARMONIC MORPHISMS AND HERMITIAN STRUCTURES ON EINSTEIN 4-MANIFOLDS.
- Authors
WOOD, JOHN C.
- Abstract
We show that a submersive harmonic morphism from an orientable Einstein 4-manifold M4 to a Riemann surface, or a conformal foliation of M4 by minimal surfaces, determines an (integrable) Hermitian structure with respect to which it is holomorphic. Conversely, any nowhere-Kähler Hermitian structure of an orientable anti-self-dual Einstein 4-manifold arises locally in this way. In the case M4=ℝ4 we show that a Hermitian structure, viewed as a map into S2, is a harmonic morphism; in this case and for S4, we determine all (submersive) harmonic morphisms to surfaces locally, and, assuming a non-degeneracy condition on the critical points, globally.
- Publication
International Journal of Mathematics, 1992, Vol 3, Issue 3, p415
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X92000187