On toric locally conformally Kähler manifolds
We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is - ∞ , and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that ev...
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| Veröffentlicht in: | Annals of global analysis and geometry 2017-06, Vol.51 (4), p.401-417 |
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| container_title | Annals of global analysis and geometry |
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| creator | Madani, Farid Moroianu, Andrei Pilca, Mihaela |
| description | We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is
-
∞
, and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold. |
| doi_str_mv | 10.1007/s10455-017-9545-5 |
| format | Article |
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-
∞
, and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.</description><identifier>ISSN: 0232-704X</identifier><identifier>EISSN: 1572-9060</identifier><identifier>DOI: 10.1007/s10455-017-9545-5</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Analysis ; Differential Geometry ; Geometry ; Global Analysis and Analysis on Manifolds ; Manifolds (mathematics) ; Mathematical Physics ; Mathematics ; Mathematics and Statistics ; Toruses</subject><ispartof>Annals of global analysis and geometry, 2017-06, Vol.51 (4), p.401-417</ispartof><rights>Springer Science+Business Media Dordrecht 2017</rights><rights>Annals of Global Analysis and Geometry is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-fff4e892b1e50fd1e458d611643c15e17bb12328084bb8fb7122ff4304d56f993</citedby><cites>FETCH-LOGICAL-c316t-fff4e892b1e50fd1e458d611643c15e17bb12328084bb8fb7122ff4304d56f993</cites><orcidid>0000-0002-9799-1036</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10455-017-9545-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10455-017-9545-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Madani, Farid</creatorcontrib><creatorcontrib>Moroianu, Andrei</creatorcontrib><creatorcontrib>Pilca, Mihaela</creatorcontrib><title>On toric locally conformally Kähler manifolds</title><title>Annals of global analysis and geometry</title><addtitle>Ann Glob Anal Geom</addtitle><description>We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is
-
∞
, and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. 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We show that the Kodaira dimension of the underlying complex manifold is
-
∞
, and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10455-017-9545-5</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0002-9799-1036</orcidid></addata></record> |
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| issn | 0232-704X 1572-9060 |
| language | eng |
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| subjects | Analysis Differential Geometry Geometry Global Analysis and Analysis on Manifolds Manifolds (mathematics) Mathematical Physics Mathematics Mathematics and Statistics Toruses |
| title | On toric locally conformally Kähler manifolds |
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