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Toric, \(U(2)\), and LeBrun metrics

dc.creatorWeber, Brian
dc.date2020-12-08
dc.date.accessioned2021-08-17T20:35:26Z
dc.date.available2021-08-17T20:35:26Z
dc.identifierhttp://revistas.ufro.cl/ojs/index.php/cubo/article/view/2474
dc.identifier10.4067/S0719-06462020000300395
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/174241
dc.descriptionThe LeBrun ansatz was designed for scalar-flat Kähler metrics with a continuous symmetry; here we show it is generalizable to much broader classes of metrics with a symmetry. We state the conditions for a metric to be (locally) expressible in LeBrun ansatz form, the conditions under which its natural complex structure is integrable, and the conditions that produce a metric that is Kähler, scalar-flat, or extremal Kähler. Second, toric Kähler metrics (such as the generalized Taub-NUTs) and \(U(2)\)-invariant metrics (such as the Fubini-Study or Page metrics) are certainly expressible in the LeBrun ansatz. We give general formulas for such transitions. We close the paper with examples, and find expressions for two examples — the exceptional half-plane metric and the Page metric — in terms of the LeBrun ansatz.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad de La Frontera. Temuco, Chile.en-US
dc.relationhttp://revistas.ufro.cl/ojs/index.php/cubo/article/view/2474/2029
dc.rightshttps://creativecommons.org/licenses/by-nc/4.0/en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 22 No. 3 (2020); 395–410en-US
dc.sourceCUBO, A Mathematical Journal; Vol. 22 Núm. 3 (2020); 395–410es-ES
dc.source0719-0646
dc.source0716-7776
dc.subjectDifferential geometryen-US
dc.subjectKähler geometryen-US
dc.subjectcanonical metricsen-US
dc.subjectansatzen-US
dc.titleToric, \(U(2)\), and LeBrun metricsen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


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