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In [KSW97a] 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 [KSW97b] and show that a nontrivial solution defines a parallel spinor on the associated hyperkähler manifold.

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Eigenvalues of the basic Dirac operator on quaternion-Kähler foliations

Habib

2006

Ann Glob Anal Geom

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Cited by 4 publications

References 24 publications

An upper bound for a Hilbert polynomial on quaternionic Kähler manifolds

An upper bound for a Hilbert polynomial on quaternionic Kähler manifolds

The First Eigenvalue of the Dirac Operator on Quaternionic Kähler Manifolds

Eigenvalues of the basic Dirac operator on quaternion-Kähler foliations

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