Type
Text
Type
Dissertation
Advisor
Lawson, Blaine | Michelsohn, Marie-Louise | Kirillov, Alexander | Rocek, Martin.
Date
2014-12-01
Keywords
Bihermitian Geometry, Generalized Kahler Geometry, Twistor Spaces | Mathematics
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76396
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Ever since the 1970's, holomorphic twistor spaces have been used to study the geometry and analysis of their base manifolds. In this dissertation, I will introduce integrable complex structures on twistor spaces fibered over complex manifolds that are equipped with certain geometrical data. The importance of these spaces will be shown to lie, for instance, in their applications to bihermitian geometry, also known as generalized Kahler geometry. (This is part of the generalized geometry program initiated by Nigel Hitchin.) By analyzing their twistor spaces, I will develop a new approach to studying bihermitian manifolds. In fact, I will demonstrate that the twistor space of a bihermitian manifold is equipped with two complex structures and natural holomorphic sections as well. This will allow me to construct tools from the twistor space that will lead, in particular, to new insights into the real and holomorphic Poisson structures on the manifold. | 68 pages
Recommended Citation
Gindi, Steven Michael, "Holomorphic Twistor Spaces and Bihermitian Geometry" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2319.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2319