Ornea, L. and Verbitsky, M. (2005) An immersion theorem for Vaisman manifolds. Mathematische Annalen, 332, pp. 121-143. (doi: 10.1007/s00208-004-0620-4)
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Abstract
A locally conformally Kähler (LCK) manifold is a complex manifold admitting a Kähler covering , with monodromy acting on by Kähler homotheties. A compact LCK manifold is Vaisman if it admits a holomorphic flow acting by non-trivial homotheties on . We prove that any compact Vaisman manifold admits a natural holomorphic immersion to a Hopf manifold (ℂ n ∖0)ℤ. As an application, we obtain that any Sasakian manifold has a contact immersion to an odd-dimensional sphere.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | UNSPECIFIED |
| Authors: | Ornea, L., and Verbitsky, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Mathematische Annalen |
| ISSN: | 0025-5831 |
| ISSN (Online): | 1432-1807 |
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