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Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...

Isotropic almost complex structures and harmonic unit vector fields

Amir Baghban, Esmaeil Abedi (2018)

Archivum Mathematicum

Isotropic almost complex structures J δ , σ define a class of Riemannian metrics g δ , σ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics g δ , 0 . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.

Isotropic curvature: A survey

Harish Seshadri (2007/2008)

Séminaire de théorie spectrale et géométrie

We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.

Isotropy representation of flag manifolds

Alekseevsky, D. V. (1998)

Proceedings of the 17th Winter School "Geometry and Physics"

A flag manifold of a compact semisimple Lie group G is defined as a quotient M = G / K where K is the centralizer of a one-parameter subgroup exp ( t x ) of G . Then M can be identified with the adjoint orbit of x in the Lie algebra 𝒢 of G . Two flag manifolds M = G / K and M ' = G / K ' are equivalent if there exists an automorphism φ : G → G such that φ ( K ) = K ' (equivalent manifolds need not be G -diffeomorphic since φ is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all flag manifolds...

Iterates of maps which are non-expansive in Hilbert's projective metric

Jeremy Gunawardena, Cormac Walsh (2003)

Kybernetika

The cycle time of an operator on R n gives information about the long term behaviour of its iterates. We generalise this notion to operators on symmetric cones. We show that these cones, endowed with either Hilbert’s projective metric or Thompson’s metric, satisfy Busemann’s definition of a space of non- positive curvature. We then deduce that, on a strictly convex symmetric cone, the cycle time exists for all maps which are non-expansive in both these metrics. We also review an analogue for the Hilbert...

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