by Grunau, Hans-Christoph, Kuehnel, Marco.
Series: 2003-09, Preprints
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 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
Hermitian-harmonic maps, non-Kaehler manifolds, non-divergence form
This paper was published in:
Math. Z. 249 , 297-327 (2005).