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Generalized complex structures on Courant algebroids [microform]
Bib ID 4653090
Format BookBook, MicroformMicroform, OnlineOnline
Author
Barton, James David
 
Online Versions
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. 
Subjects Mathematics.
Other authors/contributors The Pennsylvania State University
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001 4653090
005 20090709132306.0
008 090527s2007    miu|||||bm||||||| ||eng d
020 |a9780549438380
035 |a4653090
040 |aUMI|cUMI
100 1 |aBarton, James David.
245 1 0 |aGeneralized complex structures on Courant algebroids|h[microform].
300 |a75 p.
500 |a(UMI)AAI3298971
500 |aSource: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0349.
502 |aThesis (Ph.D.)--The Pennsylvania State University, 2007.
520 |aIn 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.
520 |aOur 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.
533 |aMicrofiche.|bAnn Arbor, Mich. :|cUniversity Microfilms International.
650 4 |aMathematics.
710 2 |aThe Pennsylvania State University.
773 0 |tDissertation Abstracts International|g69-01B.
856 |uhttp://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
984 |aANL|cmc 252 32-98971|d66004653090
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