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Harmonic morphisms in Hermitian geometry

Svensson, Martin LU (2004) In Journal für Die Reine und Angewandte Mathematik 575. p.45-68
Abstract
We prove several results on holomorphic harmonic morphisms between Hermitian manifolds. In the non-compact case, we find conditions on holomorphic maps from domains in C-2 to C to retain the harmonicity when the metric is conformally changed. We conclude that there are no non-constant harmonic morphisms from S-4 minus a point to a Riemann surface. As for the compact case, we show that holomorphic harmonic morphisms from compact Kahler manifolds of non-negative sectional curvature to Kahler manifolds which are not surfaces, are totally geodesic maps. We also provide restrictions on the Hodge numbers when such maps exist. Finally, we prove that flag manifolds carry cosymplectic structures which turn homogeneous projections into holomorphic... (More)
We prove several results on holomorphic harmonic morphisms between Hermitian manifolds. In the non-compact case, we find conditions on holomorphic maps from domains in C-2 to C to retain the harmonicity when the metric is conformally changed. We conclude that there are no non-constant harmonic morphisms from S-4 minus a point to a Riemann surface. As for the compact case, we show that holomorphic harmonic morphisms from compact Kahler manifolds of non-negative sectional curvature to Kahler manifolds which are not surfaces, are totally geodesic maps. We also provide restrictions on the Hodge numbers when such maps exist. Finally, we prove that flag manifolds carry cosymplectic structures which turn homogeneous projections into holomorphic harmonic morphisms. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal für Die Reine und Angewandte Mathematik
volume
575
pages
45 - 68
publisher
De Gruyter
external identifiers
  • wos:000224342600003
  • scopus:5644259951
ISSN
0075-4102
DOI
10.1515/crll.2004.082
language
English
LU publication?
yes
id
e1a4943f-22b8-46cd-8c66-ec7cb5ed4906 (old id 265396)
date added to LUP
2007-11-02 11:15:37
date last changed
2017-03-16 13:09:47
@article{e1a4943f-22b8-46cd-8c66-ec7cb5ed4906,
  abstract     = {We prove several results on holomorphic harmonic morphisms between Hermitian manifolds. In the non-compact case, we find conditions on holomorphic maps from domains in C-2 to C to retain the harmonicity when the metric is conformally changed. We conclude that there are no non-constant harmonic morphisms from S-4 minus a point to a Riemann surface. As for the compact case, we show that holomorphic harmonic morphisms from compact Kahler manifolds of non-negative sectional curvature to Kahler manifolds which are not surfaces, are totally geodesic maps. We also provide restrictions on the Hodge numbers when such maps exist. Finally, we prove that flag manifolds carry cosymplectic structures which turn homogeneous projections into holomorphic harmonic morphisms.},
  author       = {Svensson, Martin},
  issn         = {0075-4102},
  language     = {eng},
  pages        = {45--68},
  publisher    = {De Gruyter},
  series       = {Journal für Die Reine und Angewandte Mathematik},
  title        = {Harmonic morphisms in Hermitian geometry},
  url          = {http://dx.doi.org/10.1515/crll.2004.082},
  volume       = {575},
  year         = {2004},
}