Quaternionic Killing Spinors |
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Authors: | W Kramer U Semmelmann G Weingart |
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Institution: | (1) Mathematisches Institut der Universität Bonn, Beringstraße 1, 53115 Bonn, Germany |
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Abstract: | In 17] we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kähler manifolds. In the present article we study the limiting case, i.e. manifolds where the lower bound is attained as an eigenvalue. We give an equivalent formulation in terms of a quaternionic Killing equation and show that the only symmetric quaternionic Kähler manifolds with smallest possible eigenvalue are the quaternionic projective spaces. |
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Keywords: | Dirac operator Killing spinor quaternionic Kä hler manifold |
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