Isospectral Riemannian metrics and potentials
نویسندگان
چکیده
منابع مشابه
Isospectral Metrics and Potentials on Classical Compact Simple Lie Groups
Given a compact Riemannian manifold (M,g), the eigenvalues of the Laplace operator ∆ form a discrete sequence known as the spectrum of (M,g). (In the case the M has boundary, we stipulate either Dirichlet or Neumann boundary conditions.) We say that two Riemannian manifolds are isospectral if they have the same spectrum. For a fixed manifold M , an isospectral deformation of a metric g0 on M is...
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In this paper we construct, for n ≥ 2, arbitrarily large families of infinite towers of compact, orientable Riemannian n-manifolds which are isospectral but not isometric at each stage. In dimensions two and three, the towers produced consist of hyperbolic 2-manifolds and hyperbolic 3-manifolds, and in these cases we show that the isospectral towers do not arise from Sunada’s method.
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متن کاملCompactness of Isospectral Potentials
The Schrödinger operator −∆+V , of a compact Riemannian manifold M , has pure point spectrum. Suppose that V0 is a smooth reference potential. Various criteria are given which guarantee the compactness of all V satisfying spec(−∆+V ) = spec(−∆+V0). In particular, compactness is proved assuming an a priori bound on the Ws,2(M) norm of V , where s > n/2 − 2 and n = dimM . This improves earlier wo...
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allowed for determined boundary conditions corresponding to the standard potential . With the very useful Darboux transformation (DT) [3-6] is possible to generalize any specific standard potential and thus generate new interaction models with the same energy levels. The DT is related to the Sturm-Liouville theory [7-10], and it is easy to see the implicit presence of DT in supersymmetric quant...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1987
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1987-15541-8