Results 1 - 10 of 78

Isospectral deformations of metrics on spheres

by Carolyn S. Gordon - Invent. Math
"... Abstract. We construct non-trivial 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 ..."
Abstract - Cited by 15 (4 self) - Add to MetaCart
Abstract. We construct non-trivial 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

by Emily Proctor, Elizabeth Stanhope - 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 ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
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

by Andrzej Sitarz - 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. ..."
Abstract - Cited by 21 (2 self) - Add to MetaCart
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

by Oliver Knill
"... 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) ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
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

by Oliver Knill , 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. ..."
Abstract - Cited by 8 (5 self) - Add to MetaCart
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

by W. D. Van Suijlekom - J. Math. Phys
"... We present a new example of a finite-dimensional 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 ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
We present a new example of a finite-dimensional 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

by Victor Gayral, Bruno Iochum, Joseph C. Várilly - J. FUNCT. ANAL , 2005
"... We extend the isospectral deformations of Connes, Landi and Dubois-Violette 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 ..."
Abstract - Cited by 18 (8 self) - Add to MetaCart
We extend the isospectral deformations of Connes, Landi and Dubois-Violette 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

by Andrzej Sitarz
"... this paper we show that the isospectral deformations as defined in [3] are the special case of the Rie#el's construction [9] ..."
Abstract - Cited by 7 (0 self) - Add to MetaCart
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

by G. Popov , P. Topalov , 2001
"... We introduce a notion of weak isospectrality for continuous deformations. Consider the Laplace-Beltrami 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 ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
We introduce a notion of weak isospectrality for continuous deformations. Consider the Laplace-Beltrami 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

by Alain Connes, Giovanni Landi - Comm. Math. Phys
"... We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global features. The new examples include the instanton algebra and the ..."
Abstract - Cited by 167 (29 self) - Add to MetaCart
We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global features. The new examples include the instanton algebra
Results 1 - 10 of 78