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Two Aspects of Sasakian Geometry

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dc.contributor.advisor LeBrun, Claude en_US
dc.contributor.author Guo, Weixin en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2013-05-22T17:34:40Z
dc.date.accessioned 2015-04-24T14:46:40Z
dc.date.available 2013-05-22T17:34:40Z
dc.date.available 2015-04-24T14:46:40Z
dc.date.issued 2011-12-01 en_US
dc.identifier Guo_grad.sunysb_0771E_10788 en_US
dc.identifier.uri http://hdl.handle.net/1951/59676 en_US
dc.identifier.uri http://hdl.handle.net/11401/71247 en_US
dc.description 66 pgs en_US
dc.description.abstract Sasakian structures are the counterparts of Kahler structures in odd dimensions. A Sasakian manifold is a strictly pseudo-convex CR manifold with a Reeb vector field that generates CR automorphisms. We first study Type I deformations of Sasakian structures, which amount to different choices of Reeb vector field on a fixed CR manifold. Here we show that the CR automorphism group of a Sasakian manifold is severely constrained by mild curvature assumptions. We then study products of pairs of compact Sasakian manifolds. Such products are shown to always yield compact complex manifolds that do not admit Kahler metrics, generalizing a remarkable construction due to Calabi and Eckmann. As a consequence, any product of two compact Sasaki-Einstein manifolds yields an Einstein Hermitian metric on a compact complex manifold which does not admit Kahler metrics. This result stands in marked contrast to the situation in real dimension 4, where LeBrun showed that Einstein Hermitian metrics on compact complex surfaces are always conformally Kahler. 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 Sasakian, Type I deformation en_US
dc.title Two Aspects of Sasakian Geometry en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember LeBrun, Claude en_US
dc.contributor.committeemember Hill, Denson en_US
dc.contributor.committeemember Lawson, Blaine en_US
dc.contributor.committeemember Gu, Xianfen en_US

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