Searcharxiv⌕ Search

arXiv subjects

W. Kramer

Publications and source records attributed to W. Kramer.

3 recordsLinked to original sources
arXiv1997

The First Eigenvalue of the Dirac Operator on Quaternionic Kaehler Manifolds

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.

dg-ga↗
arXiv1997

Quaternionic Killing Spinors

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.

dg-ga↗