Type
Text
Type
Dissertation
Advisor
LeBrun, Claude
Date
2012-12-01
Keywords
Mathematics | Differential Geometry, Hyperkahler, Symmetry
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/71337
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
We consider a hyperk? hler 4n-manifold M. Using local holomorphic Darboux coordinates with respect to a compatible complex structure I on M, we find local necessary and sufficient conditions for a real smooth vector field X on M to be quaternionic Killing. We then apply this result to the case of a hyperk? hler manifold M admitting n commuting quaternionic Killing fields, X^1,... | X^n, the first n-1 of which are further assumed to be triholomorphic and quaternionically linearly independent pointwise. We then have two cases: if the self-dual part of DX^n vanishes, we get back the Hitchin-Karlhede-Lindstr??m-Roček result, and if the self-dual part of DX^n is non-zero, we obtain a partial generalization of the Boyer and Finley equation. | 79 pages
Recommended Citation
Malkoun, Joseph, "Hyperkahler 4n-Manifolds with n Commuting Quaternionic Killing Fields" (2012). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 543.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/543