Abstract:
We study holomorphic harmonic morphisms from Kähler manifolds to almost Hermitian manifolds. When the codomain is also Kähler we get restrictions on such maps in the case of constant holomorphic curvature. We also prove a Bochner-type formula for holomorphic harmonic morphisms which, under certain curvature conditions of the domain, gives insight to the structure of the vertical distribution. We thus prove that when the domain is compact and non-negatively curved, the vertical distribution is totally geodesic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 28 May 2001
Rights and permissions
About this article
Cite this article
Svensson, M. On holomorphic harmonic morphisms. manuscripta math. 107, 1–13 (2002). https://doi.org/10.1007/s002290100210
Issue Date:
DOI: https://doi.org/10.1007/s002290100210