National Library of Australia

The National Library Reading Rooms are now open at reduced hours. Find out more to plan your visit.

You must be logged in to Tag Records
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

Be the first to leave a comment!

This space is for comments to help us enhance our existing data for collection items. Comments are only reviewed by staff on a monthly basis. All enquiries should be sent via the Feedback or the Ask a Librarian links located at the top right hand side of this page.

Add your comment (you will be asked to log in)
close Can I borrow items from the Library?

You need Flash player 8+ and JavaScript enabled to view this video embedded.

You can view this on the NLA website.

close What can I get online?

You need Flash player 8+ and JavaScript enabled to view this video embedded.

You can view this on the NLA website.

close Can I get copies of items from the Library?

You need Flash player 8+ and JavaScript enabled to view this video embedded.

You can view this on the NLA website.

Aboriginal and Torres Strait Islander Flags
Aboriginal, Torres Strait Islander and other First Nations people are advised that this catalogue contains names, recordings and images of deceased people and other content that may be culturally sensitive. Please also be aware that you may see certain words or descriptions in this catalogue which reflect the author’s attitude or that of the period in which the item was created and may now be considered offensive.