T. Kobayashi, Hidden symmetries and spectrum of the Laplacian on an indefinite Riemannian manifold, Spectral Analysis in Geometry and Number Theory (in honor of Professor Sunada) (M. Kotani, H. Naito, and T. Tate, eds.), Contemp. Math., vol. 484, Amer. Math. Soc., Providence, RI, 2009, pp. 73-87.

Inspired by Sunada's problem, we find a six dimensional, non-compact Γ-periodic Riemannian manifold that admits countably many discrete spectra of the Laplacian. This manifold also carries a three dimensional complex structure with indefinite Kähler metric. We observe a hidden symmetry in the sense that the automorphism group of the indefinite Kähler metric is larger than the group of Riemannian isometries. This very symmetry breaks a path to the theory of discontinuous groups for non-Riemannian manifolds and the theory of discrete decomposable branching laws of unitary representations.
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