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Hyperkahler 4n-Manifolds with n Commuting Quaternionic Killing Fields

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dc.contributor.advisor LeBrun, Claude en_US
dc.contributor.author Malkoun, Joseph en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2013-05-22T17:35:12Z
dc.date.accessioned 2015-04-24T14:47:05Z
dc.date.available 2013-05-22T17:35:12Z
dc.date.available 2015-04-24T14:47:05Z
dc.date.issued 2012-12-01
dc.identifier Malkoun_grad.sunysb_0771E_10833 en_US
dc.identifier.uri http://hdl.handle.net/1951/59780 en_US
dc.identifier.uri http://hdl.handle.net/11401/71337 en_US
dc.description 79 pg. en_US
dc.description.abstract We consider a hyperk? hler 4n-manifold M. Using local holomorphic Darboux coordinates with respect to a compatible complex structure I on M, we find local necessary and sufficient conditions for a real smooth vector field X on M to be quaternionic Killing. We then apply this result to the case of a hyperk? hler manifold M admitting n commuting quaternionic Killing fields, X^1,..., X^n, the first n-1 of which are further assumed to be triholomorphic and quaternionically linearly independent pointwise. We then have two cases: if the self-dual part of DX^n vanishes, we get back the Hitchin-Karlhede-Lindstr??m-Roček result, and if the self-dual part of DX^n is non-zero, we obtain a partial generalization of the Boyer and Finley equation. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Mathematics en_US
dc.subject.other Differential Geometry, Hyperkahler, Symmetry en_US
dc.title Hyperkahler 4n-Manifolds with n Commuting Quaternionic Killing Fields en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US

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