Biharmonic holomorphic maps and conformally Kahler geometry
Differential Geometry
2012-04-11 v1
Abstract
We give conditions on the Lee vector field of an almost Hermitian manifold such that any holomorphic map from this manifold into a (1,2)-symplectic manifold must satisfy the fourth-order condition of being biharmonic, hence generalizing the Lichnerowicz theorem on harmonic maps. These third-order non-linear conditions are shown to greatly simplify on l.c.K. manifolds and construction methods and examples are given in all dimensions.
Cite
@article{arxiv.1204.2104,
title = {Biharmonic holomorphic maps and conformally Kahler geometry},
author = {M. Benyounes and E. Loubeau and R. Slobodeanu},
journal= {arXiv preprint arXiv:1204.2104},
year = {2012}
}
Comments
14 pages