02302cam a2200265 4500001000800000005001700008008004100025020001800066035001200084040001300096100002500109245007100134300001000205500002000215500008900235502006100324520093600385520034501321533007401666650001701740710003901757773005001796856015201846984003801998465309020090709132306.0090527s2007 miu|||||bm||||||| ||eng d a9780549438380 a4653090 aUMIcUMI1 aBarton, James David.10aGeneralized complex structures on Courant algebroidsh[microform]. a75 p. a(UMI)AAI3298971 aSource: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0349. aThesis (Ph.D.)--The Pennsylvania State University, 2007. 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. 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. aMicrofiche.bAnn Arbor, Mich. :cUniversity Microfilms International. 4aMathematics.2 aThe Pennsylvania State University.0 tDissertation Abstracts Internationalg69-01B. 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 aANLcmc 252 32-98971d66004653090