Kähler structures and convexity properties of coadjoint orbits

Karl-Hermann Neeb

doi:10.1515/form.1995.7.349

Deformation classes in generalized Kähler geometry

Complex Manifolds ◽

10.1515/coma-2020-0101 ◽

2020 ◽

Vol 7 (1) ◽

pp. 241-256

Author(s):

Matthew Gibson ◽

Jeffrey Streets

Keyword(s):

Symmetry Group ◽

Ricci Flow ◽

Kahler Geometry ◽

Poisson Tensor ◽

Natural Extensions ◽

Generalized Kähler Geometry ◽

Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

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On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Mathematics ◽

10.3390/math9040310 ◽

2021 ◽

Vol 9 (4) ◽

pp. 310 ◽

Cited By ~ 1

Author(s):

Pedro Ortiz ◽

Juan Carlos Trillo

Keyword(s):

Initial Data ◽

Numerical Experiments ◽

Approximation Order ◽

Piecewise Polynomial ◽

Nonuniform Grids ◽

Uniform Grids ◽

Reconstruction Operator ◽

Convexity Properties ◽

Second Degree

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

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Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

Journal of High Energy Physics ◽

10.1007/jhep12(2020)189 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Fridrich Valach ◽

Donald R. Youmans

Keyword(s):

Quantum Mechanics ◽

Partition Function ◽

Gauge Group ◽

Path Integral ◽

Coadjoint Orbits ◽

Two Dimensional ◽

Edge States ◽

Class Constraint ◽

Action Functional ◽

Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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Location and shape of a rectangular facility in ℝn. Convexity properties. Convexity properties

Mathematical Programming ◽

10.1007/bf02680563 ◽

1998 ◽

Vol 83 (1-3) ◽

pp. 277-290 ◽

Cited By ~ 5

Author(s):

E. Carrizosa ◽

M. Muñoz-Márquez ◽

J. Puerto

Keyword(s):

Convexity Properties

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The Darboux coordinate system and Holstein–Primakoff representations on Kähler manifolds

Canadian Journal of Physics ◽

10.1139/p06-081 ◽

2006 ◽

Vol 84 (10) ◽

pp. 891-904

Author(s):

J R Schmidt

Keyword(s):

Coordinate System ◽

Lie Groups ◽

Lie Algebra ◽

Poisson Structure ◽

Kähler Manifolds ◽

Coadjoint Orbits ◽

Kahler Manifolds ◽

Canonical Transformations ◽

Kahler Geometry

The Kahler geometry of minimal coadjoint orbits of classical Lie groups is exploited to construct Darboux coordinates, a symplectic two-form and a Lie–Poisson structure on the dual of the Lie algebra. Canonical transformations cast the generators of the dual into Dyson or Holstein–Primakoff representations.PACS Nos.: 02.20.Sv, 02.30.Ik, 02.40.Tt

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