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Twistor theory of hyper-K{ä}hler metrics with hidden symmetries

Abstract:

We briefly review the hierarchy for the hyper-K\"ahler equations and define a notion of symmetry for solutions of this hierarchy. A four-dimensional hyper-K\"ahler metric admits a hidden symmetry if it embeds into a hierarchy with a symmetry. It is shown that a hyper-K\"ahler metric admits a hidden symmetry if it admits a certain Killing spinor. We show that if the hidden symmetry is tri-holomorphic, then this is equivalent to requiring symmetry along a higher time and the hidden symmetry det...

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Publication status:
Published

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Publisher copy:
10.1063/1.1588466

Authors


Dunajski, M More by this author
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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
J.Math.Phys.
Volume:
44
Issue:
8
Pages:
3430-3454
Publication date:
2003-01-16
DOI:
ISSN:
0022-2488
URN:
uuid:d46273ca-a63d-4ab0-ab9f-9c581d8c4975
Source identifiers:
26376
Local pid:
pubs:26376
Language:
English
Keywords:

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