Quaternionic Killing Spinors

Details Quaternionic Killing Spinors Quaternionic Killing Spinors

1997-06-27

arxiv.org/abs/dg-ga/9706017v1

Mathematics

Differential Geometry

17 pages, LaTeX2e, fullpage style

Scientific paper

In a previous article we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler 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 Kaehler manifolds with smallest possible eigenvalue are the quaternionic projective spaces.

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