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## Automorphisms of locally conformally Kahler manifolds

International Mathematics Research Notices. 2012. No. 4. P. 894-903.

Liviu O., Verbitsky M.

A manifold M is locally conformally Kähler (LCK), if it admits a Kähler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and the lifting of this action to the Kähler cover is not isometric. We show that admits an automorphic Kähler potential, and hence (for dimℂ M > 2) the manifold M can be embedded to a Hopf manifold.

Research target:
Philosophy, Ethics, and Religious Studies

Language:
English

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Marshakov A., Mironov A., Morozov A., Journal of High Energy Physics 2009 No. 11(048) P. 1-15

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Feigin E., Fourier G., Littelmann P., International Mathematics Research Notices 2011 Vol. 2011 No. 24 P. 5760-5784

We study the PBW filtration on the highest weight representations V(λ) of sp2n. This
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Kolesnikov A., Banakh T., Bogachev V., Functional Analysis and Its Applications 2004 P. 23-47

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The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(ˆR, ˆ F) defined by a pair of compatible
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Rudakov A. N., Шафаревич И., Успехи математических наук 1978 Т. 33 № 1(199) С. 227-228

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Finkelberg M. V., Gaitsgory D., Kuznetsov A., Publications of the Research Institute for Mathematical Sciences 2003 Vol. 39 No. 4 P. 721-766

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Series C., Bufetov A. I., Mathematical Proceedings of the Cambridge Philosophical Society 2011 Vol. 151 No. 1 P. 145-159

We use Series' Markovian coding for words in Fuchsian groups and the
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Zotov A., Levin A., Olshanetsky M., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2009 Vol. 5 No. 065 P. 1-22

Modifications of bundles over complex curves is an operation that allows one to
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Goldengorin B. I., European Journal of Operational Research 2009 Vol. 198 No. 1 P. 102-112

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Rudakov A. N., Journal of Algebraic Geometry 1997 Vol. 197 No. 1 P. 231-245

The main goal of the article is to give the definition of algebraic stability that
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Nekrasov N., Marshakov A., Journal of High Energy Physics 2007 No. 0701 P. 104

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Rudakov A. N., Шафаревич И., Успехи математических наук 1978 Т. 33 № 6(204) С. 231-232

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Braverman A., Finkelberg M. V., Duke Mathematical Journal 2010 Vol. 152 No. 1 P. 175-206

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"The universal enveloping algebra of any simple Lie algebra g contains a
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