The First Eigenvalue of the Dirac Operator on Quaternionic Kaehler Manifolds

Details The First Eigenvalue of the Dirac Operator on Quaternionic Kaehler Manifolds The First Eigenvalue of the Dirac Operator on Quaternionic Kaehler Manifolds

1997-09-10

arxiv.org/abs/dg-ga/9709014v1

Mathematics

Differential Geometry

19 pages, LaTeX2e, fullpage style

Scientific paper

10.1007/s002200050504

In a previous paper we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler 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 and show that a nontrivial solution defines a parallel spinor on the associated hyperkaehler manifold.

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