Harmonic morphisms in Hermitian geometry
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/265396
- author
- Svensson, Martin LU
- organization
- publishing date
- 2004
- 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
- 2016-04-01 15:27:13
- date last changed
- 2022-01-28 05:27:05
@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}},
doi = {{10.1515/crll.2004.082}},
volume = {{575}},
year = {{2004}},
}