Isospectral metrics and potentials on classical compact simple Lie groups

Details Isospectral metrics and potentials on classical compact simple Lie groups Isospectral metrics and potentials on classical compact simple Lie groups

2004-08-11

arxiv.org/abs/math/0408152v1

Mathematics

Differential Geometry

13 pages

Scientific paper

We prove the existence of multiparameter isospectral deformations of metrics on SO(n) $(n = 9$ and $n\geq 11)$, SU(n) $(n\geq 8)$, and $Sp(n)$ $(n\geq 4)$. For these examples, we follow a metric construction developed by Schueth who had given one-parameter families of isospectral metrics on orthogonal and unitary groups. Our multiparameter families are obtained by a new proof of nontriviality establishing a generic condition for nonisometry of metrics arising from the construction. We also show the existence of non-congruent pairs of isospectral potentials and nonisometric pairs of isospectral conformally equivalent metrics on $Sp(n)$ for $n\geq 6$.

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