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Continuous families of isospectral metrics on simply connected manifolds.

Schueth, Dorothee — 1999

Annals of Mathematics. Second Series

Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds.

Dorothee Schueth — 1995

Commentarii mathematici Helvetici

Symplectic rigidity of geodesic flows on two-step nilmanifolds

Carolyn S. Gordon; Yiping Mao; Dorothee Schueth — 1997

Annales scientifiques de l'École Normale Supérieure

Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent

Carolyn Gordon; William Kirwin; Dorothee Schueth; David Webb — 2010

Annales de l’institut Fourier

We construct pairs of compact Kähler-Einstein manifolds $(M_{i}, g_{i}, ω_{i}) (i = 1, 2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_{i} = ⋀^{n} T^{*} M_{i}$ has Chern class $[ω_{i} / 2 π]$ , and for each positive integer $k$ the tensor powers $L_{1}^{\otimes k}$ and $L_{2}^{\otimes k}$ are isospectral for the bundle Laplacian associated with the canonical connection, while $M_{1}$ and $M_{2}$ – and hence $T^{*} M_{1}$ and $T^{*} M_{2}$ – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent....

Spectral isolation of bi-invariant metrics on compact Lie groups

Carolyn S. Gordon; Dorothee Schueth; Craig J. Sutton — 2010

Annales de l’institut Fourier

We show that a bi-invariant metric on a compact connected Lie group $G$ is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric $g_{0}$ on $G$ there is a positive integer $N$ such that, within a neighborhood of $g_{0}$ in the class of left-invariant metrics of at most the same volume, $g_{0}$ is uniquely determined by the first $N$ distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where $G$ is simple, $N$ can be chosen to be two....

Isospectral deformations of closed riemannian manifolds with different scalar curvature

Carolyn S. Gordon; Ruth Gornet; Dorothee Schueth; David L. Webb; Edward N. Wilson — 1998

Annales de l'institut Fourier

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on $S^{n} \times T^{m}$ , where $T^{m}$ is a torus of dimension $m \geq 2$ and $S^{n}$ is a sphere of dimension $n \geq 4$ . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

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