Physics – Mathematical Physics
Scientific paper
2011-08-18
SIGMA 7 (2011), 080, 8 pages
Physics
Mathematical Physics
Scientific paper
10.3842/SIGMA.2011.080
For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in ${\mathbb R}^2$ which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method ("transplantability") using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counter examples can occur. In fact, the main result is a corollary of a result on Schreier coset graphs of 2-transitive groups.
Schillewaert Jeroen
Thas Koen
No associations
LandOfFree
The 2-Transitive Transplantable Isospectral Drums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The 2-Transitive Transplantable Isospectral Drums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The 2-Transitive Transplantable Isospectral Drums will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-180701