Para-Holomorphic Algebroids and Para-Complex Connections
dc.contributor.author | Patterson, Aidan | |
dc.date.accessioned | 2021-12-17T16:44:36Z | |
dc.date.available | 2021-12-17T16:44:36Z | |
dc.date.issued | 2021-12-17 | |
dc.date.submitted | 2021-12-08 | |
dc.description.abstract | The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost para-complex structure, and use this to define a notion of para-holomorphic algebroid. We investigate connections on para-holomorphic algebroids and determine an appropriate sense in which they can be para-complex. Finally, we show through a series of examples how the theory of exact para-holomorphic algebroids with a para-complex connection is a generalization of both para-Kähler geometry and the theory of Poisson-Lie groups. | en |
dc.identifier.uri | http://hdl.handle.net/10012/17772 | |
dc.language.iso | en | en |
dc.pending | false | |
dc.publisher | University of Waterloo | en |
dc.subject | Complex Geometry | en |
dc.subject | Courant Algebroid | en |
dc.subject | Lie Algebroid | en |
dc.subject | Lie Bialgebroid | en |
dc.subject | Para-Hermitian Connection | en |
dc.subject | Poisson-Lie Group | en |
dc.subject | Para-Kähler Geometry | en |
dc.title | Para-Holomorphic Algebroids and Para-Complex Connections | en |
dc.type | Master Thesis | en |
uws-etd.degree | Master of Mathematics | en |
uws-etd.degree.department | Pure Mathematics | en |
uws-etd.degree.discipline | Pure Mathematics | en |
uws-etd.degree.grantor | University of Waterloo | en |
uws-etd.embargo.terms | 0 | en |
uws.contributor.advisor | Moraru, Ruxandra | |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.peerReviewStatus | Unreviewed | en |
uws.published.city | Waterloo | en |
uws.published.country | Canada | en |
uws.published.province | Ontario | en |
uws.scholarLevel | Graduate | en |
uws.typeOfResource | Text | en |