Generalized complex structures on Courant algebroids [microform]
- Bib ID:
- 4653090
- Format:
- Book and Microform
- Author:
- Barton, James David
- Online Version:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3298971
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- Description:
- 75 p.
- ISBN:
- 9780549438380
- Summary:
-
In this thesis we study generalized complex structures defined on Lie bialgebroids, and arbitrary Courant algebroids. This thesis consists of two parts: the first deals with the generalized complex structures on Courant algebroids, while the second discusses generalized complex submanifolds. The basic examples of generalized complex structures are given, and certain classes of Poisson-Nijenhuis manifolds are described using generalized complex structures. The Poisson structure arising from a generalized complex structure is also defined explicitly. Generalized complex structures on arbitrary Courant algebroids are also described using generating operators and spinors. A generating operator for the Courant algebroid of a Lie bialgebroid is also given. In the second part we introduce the notion of twisted generalized complex submanifolds and describe an equivalent characterization in terms of Poisson-Dirac submanifolds.
Our characterization recovers a result of Vaisman [38]. An equivalent characterization is also given in terms of spinors. As a consequence, we show that the fixed locus of an involution preserving a twisted generalized complex structure is a twisted generalized complex submanifold. Lastly, we also discuss generalized Kahler submanifolds.
- Notes:
-
- (UMI)AAI3298971
- Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0349.
- Thesis (Ph.D.)--The Pennsylvania State University, 2007.
- Reproduction:
- Microfiche. Ann Arbor, Mich. : University Microfilms International.
- Subject:
- Mathematics
- Other authors/contributors:
- The Pennsylvania State University
- Copyright:
-
In Copyright
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Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 2007
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