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 | References | Similar Articles | Additional Information

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 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