The spectrum of the Dirac operator on SU2/Q8

by Nicolas Ginoux

manuscripta math. 125 (2008), no. 3, 383-409

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Abstract: We compute the fundamental Dirac operator for the three-parameter-family of homogeneous Riemannian metrics and the four different spin structures on SU2/Q8, where Q8 denotes the group of quaternions. We deduce its spectrum for the Berger metrics and show the sharpness of Christian Bär's upper bound for the smallest Dirac eigenvalue in the particular case where SU2/Q8 is a homogeneous minimal hypersurface of S^4.

Nicolas Ginoux, 10.03.2011