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On the holomorphicity of harmonic maps from compact Kähler manifolds to hyperbolic Riemann surfaces


Author: Kaoru Ono
Journal: Proc. Amer. Math. Soc. 102 (1988), 1071-1076
MSC: Primary 58E20; Secondary 32H20, 53C55, 58C10
DOI: https://doi.org/10.1090/S0002-9939-1988-0934892-9
MathSciNet review: 934892
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Abstract: We give a sufficient condition in order that a harmonic map from a compact Kähler manifold with negative first Chern class to a compact hyperbolic Riemann surface be $ \pm$ holomorphic. The above condition generalizes that of Eells and Wood concerning harmonic maps between Riemann surfaces. As a corollary we get a generalization of Kneser's theorem.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934892-9
Keywords: Harmonic map, holomorphic map, Kähler manifold, Einstein-Hermitian vector bundle, semistable vector bundle
Article copyright: © Copyright 1988 American Mathematical Society

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