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On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds

Hans-Christoph Grunau·Marco Kuehnel
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Abstract

On non-Kähler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of noncompact complete preimage and target manifolds is considered. We give conditions for existence and uniqueness of Hermitian-harmonic maps and solutions of the corresponding parabolic system, which observe the non-divergence form of the underlying equations. Numerous examples illustrate the theoretical results and the fundamental difference to harmonic maps.

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Hans-Christoph Grunau, Marco Kuehnel. 2003-03-12. On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds. https://arxiv.org/abs/math/0303137

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