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    Hyperkahler 4n-Manifolds with n Commuting Quaternionic Killing Fields

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    Malkoun_grad.sunysb_0771E_10833.pdf (492.3Kb)
    Date
    1-Dec-12
    Author
    Malkoun, Joseph
    Publisher
    The Graduate School, Stony Brook University: Stony Brook, NY.
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    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.
    Description
    79 pg.
    URI
    http://hdl.handle.net/1951/59780
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    • Stony Brook Theses & Dissertations [SBU] [1955]

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