A universal lower bound for the first eigenvalue of the Dirac operator on quaternionic Kähler manifolds
نویسنده
چکیده
A universal lower bound for the first positive eigenvalue of the Dirac operator on a compact quaternionic Kähler manifold M of positive scalar curvature is calculated. It is shown that it is equal to the first positive eigenvalue on the quaternionic projective space. For this, the horizontal tangent bundle on the canonical SO(3)-bundle over M is equipped with a hyperkählerian structure and the corresponding splitting of the horizontal spinor bundle is considered. The desired estimate is obtained by looking at hyperkählerian twistor operators on horizontal spinors.
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