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Analogues of Kähler geometry on Sasakian manifolds

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dc.contributor.advisor Shing-Tung Yau. en_US Tievsky, Aaron M en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2009-04-29T17:29:06Z 2009-04-29T17:29:06Z 2008 en_US 2008 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. en_US
dc.description Includes bibliographical references (p. 53-54). en_US
dc.description.abstract A Sasakian manifold S is equipped with a unit-length, Killing vector field ( which generates a one-dimensional foliation with a transverse Kihler structure. A differential form a on S is called basic with respect to the foliation if it satisfies [iota][epsilon][alpha] = [iota][epsilon]d[alpha] = 0. If a compact Sasakian manifold S is regular, i.e. a circle bundle over a compact Kähler manifold, the results of Hodge theory in the Kahler case apply to basic forms on S. Even in the absence of a Kähler base, there is a basic version of Hodge theory due to El Kacimi-Alaoui. These results are useful in trying to imitate Kähler geometry on Sasakian manifolds; however, they have limitations. In the first part of this thesis, we will develop a "transverse Hodge theory" on a broader class of forms on S. When we restrict to basic forms, this will give us a simpler proof of some of El Kacimi-Alaoui's results, including the basic dd̄-lemma. In the second part, we will apply the basic dd̄-lemma and some results from our transverse Hodge theory to conclude (in the manner of Deligne, Griffiths, and Morgan) that the real homotopy type of a compact Sasakian manifold is a formal consequence of its basic cohomology ring and basic Kähler class. en_US
dc.description.statementofresponsibility by Aaron Michael Tievsky. en_US
dc.format.extent 54 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Analogues of Kähler geometry on Sasakian manifolds en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 316799845 en_US

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