Abstract:
In [15] we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kähler manifolds. In the present article we show that the only manifolds in the limit case, i.–e. the only manifolds where the lower bound is attained as an eigenvalue, are the quaternionic projective spaces. We use the equivalent formulation in terms of the quaternionic Killing equation introduced in [16] and show that a nontrivial solution defines a parallel spinor on the associated hyperkähler manifold.
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Received: 2 February 1998 / Accepted: 8 May 1998
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Kramer, W., Semmelmann, U. & Weingart, G. The First Eigenvalue of the Dirac Operator on Quaternionic Kähler Manifolds. Comm Math Phys 199, 327–349 (1998). https://doi.org/10.1007/s002200050504
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DOI: https://doi.org/10.1007/s002200050504