## 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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related papers (discontinuous groups) |

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© Toshiyuki Kobayashi