Mathematics – Differential Geometry
Scientific paper
2005-10-10
Mathematics
Differential Geometry
43 pages. Completely new version. The constructions developed in the previous version are moved to a new paper
Scientific paper
The intertwining operator constructed in [Sz1,Sz2] does not appear in the right form. It is established there by using only the anticommutators. The correct operator must involve all endomorphisms, which are unified by the Z-Fourier transform. Although some of the correct elements of the previous constructions are kept, this idea is established by a new technique which yields the various isospectrality theorems stated in the papers on a much larger scale. The new results include new isospectrality examples living on sphere$X$ball- and sphere$X$sphere-type manifolds. Among them, there are such discrete isospectrality families where one of the members is homogeneous while the others are locally inhomogeneous (striking examples). Furthermore, a large class of new isospectrality families are constructed by $\sigma$ deformations.
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