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Locally conformally Kähler manifolds with potential
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ornea, Liviu Verbitsky, Misha |
| Copyright Year | 2004 |
| Abstract | A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold M̃ with the deck transform group acting conformally on M̃ . If M admits a holomorphic flow, acting on M̃ conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vaisman manifolds is stable under small deformations. We define a new class of LCK-manifolds, called LCK manifolds with potential, which is closed under small deformations. All Vaisman manifolds are LCK with potential. We show that an LCK-manifold with potential admits a covering which can be compactified to a Stein variety by adding one point. This is used to show that any LCK manifold M with potential, dimM > 3, can be embedded to a Hopf manifold, thus improving on similar results for Vaisman and Sasakian manifolds ([OV2]). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0407231v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0407231v3.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0407231v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0407231v4.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0407231v5.pdf |
| Alternate Webpage(s) | http://gta.math.unibuc.ro/pages/ov_matan2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
