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.[ related papers (branching laws) | related papers (discontinuous groups) | full text(pdf) ]
© Toshiyuki Kobayashi