Para-Holomorphic Algebroids and Para-Complex Connections
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Date
2021-12-17
Authors
Patterson, Aidan
Advisor
Moraru, Ruxandra
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
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.
Description
Keywords
Complex Geometry, Courant Algebroid, Lie Algebroid, Lie Bialgebroid, Para-Hermitian Connection, Poisson-Lie Group, Para-Kähler Geometry