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78
Isospectral deformations of metrics on spheres
 Invent. Math
"... Abstract. We construct nontrivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in R n for every n ≥ 9. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular, they can be chosen to be positively curved. The metrics on ..."
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Cited by 15 (4 self)
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Abstract. We construct nontrivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in R n for every n ≥ 9. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular, they can be chosen to be positively curved. The metrics
An isospectral deformation on an infranilorbifold
 MR2761691 (2012a:58060), Zbl 1204.58028
"... Abstract. We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada’s Theorem due to DeTurck and Gordon. 200 ..."
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Cited by 2 (0 self)
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Abstract. We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada’s Theorem due to DeTurck and Gordon
Twists And Spectral Triples For Isospectral Deformations
 Lett. Math. Phys
"... We construct explicitly the symmetries of the isospectral deformations as twists of Lie algebras and demonstrate that they are isometries of the deformed spectral triples. ..."
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Cited by 21 (2 self)
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We construct explicitly the symmetries of the isospectral deformations as twists of Lie algebras and demonstrate that they are isometries of the deformed spectral triples.
ISOSPECTRAL DEFORMATIONS OF THE DIRAC OPERATOR
"... Abstract. We give more details about an integrable system [26] in which the Dirac operator D = d + d ∗ on a graph G or manifold M is deformed using a Hamiltonian system D ′ = [B, h(D)] with B = d − d ∗ + βib. The deformed operator D(t) = d(t) + b(t) + d(t) ∗ defines a new exterior derivative d(t) ..."
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Cited by 1 (1 self)
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Abstract. We give more details about an integrable system [26] in which the Dirac operator D = d + d ∗ on a graph G or manifold M is deformed using a Hamiltonian system D ′ = [B, h(D)] with B = d − d ∗ + βib. The deformed operator D(t) = d(t) + b(t) + d(t) ∗ defines a new exterior derivative d(t) and
Isospectral Deformations of Random Jacobi Operators
, 1993
"... We show the integrability of infinite dimensional Hamiltonian systems obtained by making isospectral deformations of random Jacobi operators over an abstract dynamical system. The time 1 map of these so called random Toda flows can be expressed by a QR decomposition. ..."
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Cited by 8 (5 self)
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We show the integrability of infinite dimensional Hamiltonian systems obtained by making isospectral deformations of random Jacobi operators over an abstract dynamical system. The time 1 map of these so called random Toda flows can be expressed by a QR decomposition.
The noncommutative Lorentzian cylinder as an isospectral deformation
 J. Math. Phys
"... We present a new example of a finitedimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes’ character formula for the cylinder. In the second part, we discuss ..."
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Cited by 4 (1 self)
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We present a new example of a finitedimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes’ character formula for the cylinder. In the second part, we discuss
Dixmier traces on noncompact isospectral deformations
 J. FUNCT. ANAL
, 2005
"... We extend the isospectral deformations of Connes, Landi and DuboisViolette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group R l. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of fu ..."
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Cited by 18 (8 self)
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We extend the isospectral deformations of Connes, Landi and DuboisViolette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group R l. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals
Rieffel's Deformation Quantization and Isospectral Deformations
"... this paper we show that the isospectral deformations as defined in [3] are the special case of the Rie#el's construction [9] ..."
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Cited by 7 (0 self)
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this paper we show that the isospectral deformations as defined in [3] are the special case of the Rie#el's construction [9]
Invariants of isospectral deformations and spectral rigidity
, 2001
"... We introduce a notion of weak isospectrality for continuous deformations. Consider the LaplaceBeltrami operator on a compact Riemannian manifold with boundary with Robin boundary conditions. Given a Kronecker invariant torus Λ of the billiard ball map with a vector of rotation satisfying a Diophant ..."
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Cited by 3 (2 self)
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We introduce a notion of weak isospectrality for continuous deformations. Consider the LaplaceBeltrami operator on a compact Riemannian manifold with boundary with Robin boundary conditions. Given a Kronecker invariant torus Λ of the billiard ball map with a vector of rotation satisfying a
Noncommutative manifolds, the instanton algebra and isospectral deformations
 Comm. Math. Phys
"... We give new examples of noncommutative manifolds that are less standard than the NCtorus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have nontrivial global features. The new examples include the instanton algebra and the ..."
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Cited by 167 (29 self)
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We give new examples of noncommutative manifolds that are less standard than the NCtorus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have nontrivial global features. The new examples include the instanton algebra
Results 1  10
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