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An immersion theorem for Vaisman manifolds

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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 (ℂn∖0)ℤ. As an application, we obtain that any Sasakian manifold has a contact immersion to an odd-dimensional sphere.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Bucharest, 14 Academiei str., 70109, Bucharest, Romania

    Liviu Ornea

  2. Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow, Scotland

    Misha Verbitsky

Authors
  1. Liviu Ornea
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  2. Misha Verbitsky
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Correspondence to Misha Verbitsky.

Additional information

Mathematics Subject Classification (2000): 53C55, 14E25, 53C25

Liviu Ornea is member of EDGE, Research Training Network HRPN-CT-2000-00101, supported by the European Human Potential Programme.

Misha Verbitsky is an EPSRC advanced fellow supported by CRDF grant RM1-2354-MO02 and EPSRC grant GR/R77773/01.

Both authors acknowledge financial support from Ecole Polytechnique (Palaiseau).

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Ornea, L., Verbitsky, M. An immersion theorem for Vaisman manifolds. Math. Ann. 332, 121–143 (2005). https://doi.org/10.1007/s00208-004-0620-4

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  • DOI: https://doi.org/10.1007/s00208-004-0620-4

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