- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Locally conformally Kähler manifolds with holomorphic...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Locally conformally Kähler manifolds with holomorphic Lee field Moroianu, Andrei
Description
A locally conformally Kähler (LCK) manifold is a compact Hermitian manifold $(M,g,J)$ whose fundamental 2-form $\omega:=g(J\cdot,\cdot)$ verifies $d\omega=\theta\wedge\omega$ for a certain closed 1-form $\theta$ called the Lee form. We study here LCK manifolds whose Lee vector field (the metric dual of $\theta$) is holomorphic. We will show that if its norm is constant or if its divergence vanishes, then the metric is Vaisman, i.e. the Lee form is parallel with respect to the Levi-Civita connection of $g$. We will then give examples of non-Vaisman LCK manifolds with holomorphic Lee field, and we classify all such structures on manifolds of Vaisman type. These results have been obtained in collaboration with F. Madani, S. Moroianu, L. Ornea and M. Pilca.
Item Metadata
| Title |
Locally conformally Kähler manifolds with holomorphic Lee field
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2019-10-28T16:52
|
| Description |
A locally conformally Kähler (LCK) manifold is a
compact Hermitian manifold $(M,g,J)$ whose fundamental 2-form
$\omega:=g(J\cdot,\cdot)$ verifies $d\omega=\theta\wedge\omega$
for a certain closed 1-form $\theta$ called the Lee form. We
study here LCK manifolds whose Lee vector field (the metric dual
of $\theta$) is holomorphic. We will show that if its norm is
constant or if its divergence vanishes, then the metric is
Vaisman, i.e. the Lee form is parallel with respect to the
Levi-Civita connection of $g$. We will then give examples of
non-Vaisman LCK manifolds with holomorphic Lee field, and we
classify all such structures on manifolds of Vaisman type. These
results have been obtained in collaboration with F. Madani, S.
Moroianu, L. Ornea and M. Pilca.
|
| Extent |
60.0 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: CNRS
|
| Series | |
| Date Available |
2020-04-26
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0389981
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International