Mathematics – Differential Geometry
Scientific paper
2004-07-25
Geom. Topol. 8(2004) 1227-1242
Mathematics
Differential Geometry
Freely redistributable version (GNU FDL). Differs only very slightly from the version published by Geometry and Topology at
Scientific paper
We introduce a pair of isospectral but non-isometric compact flat 3-manifolds called Tetra (a tetracosm) and Didi (a didicosm). The closed geodesics of Tetra and Didi are very different. Where Tetra has two quarter-twisting geodesics of the shortest length, Didi has four half-twisting geodesics. Nevertheless, these spaces are isospectral. This isospectrality can be proven directly by matching eigenfunctions having the same eigenvalue. However, the real interest of this pair--and what led us to discover it--is the way isospectrality emerges from the Selberg trace formula, as the result of a delicate interplay between the lengths and twists of closed geodesics.
Doyle Peter G.
Rossetti Juan Pablo
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