Term of Award

Spring 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Yi Lin

Committee Member 1

Xiangdong Xie

Committee Member 2

Francois Ziegler

Abstract

A generalized complex structure, as introduced by N. Hitchin, is a common generalization of both symplectic and complex structures. Generalized complex geometry provides a natural geometric framework to understand certain recent developments in string physics, and has developed into an active area of research. Very recently, an odd dimensional analogue of a generalized complex structure, namely a generalized contact structure, has been introduced in the works of Vaizman, Poon and Wade. In this thesis, we survey the recent works on generalized contact structures. More importantly, we prove a local normal form theorem of a generalized contact structure. This result, which is a joint work with Yi Lin, is original.

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