by Grunau, Hans-Christoph, Kuehnel, Marco.

**Series:** 2003-09, Preprints

- MSC:
- 53C42 Immersions (minimal, prescribed curvature, tight, etc.)
- 35J60 Nonlinear elliptic equations
- 35K55 Nonlinear parabolic equations

**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 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.

**Keywords:**

Hermitian-harmonic maps, non-Kaehler manifolds, non-divergence form

**This paper was published in:**

Math. Z. 249 , 297-327 (2005).