The real Jacobi group revisited

DOI10.3842/SIGMA.2019.096zbMath1436.32044arXiv1903.10721MaRDI QIDQ2297926

Stefan Berceanu

Publication date: 20 February 2020

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.10721

zbMATH Keywords

Jacobi groupinvariant metricbalanced metricSiegel-Jacobi upper half-plane

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Kähler manifolds (32Q15) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Geodesics in global differential geometry (53C22)

Related Items (2)

Invariant metric on the extended Siegel-Jacobi upper half space ⋮ Hamiltonian systems on almost cosymplectic manifolds

Cites Work

• General concept of quantization
• The classification of naturally reductive homogeneous spaces in dimensions \(n\leq 6\)
• Berezin quantization of homogeneous bounded domains
• Moment maps, scalar curvature and quantization of Kähler manifolds
• Balanced metric and Berezin quantization on the Siegel-Jacobi ball
• The theory of Jacobi forms
• On contact manifolds
• Higher order parallel surfaces in Bianchi-Cartan-Vranceanu spaces
• The fundamental conjecture for homogeneous Kähler manifolds
• On differentiable manifolds with contact metric structures
• Contact manifolds in Riemannian geometry
• Curvatures of left invariant metrics on Lie groups
• Coherent state representations of nilpotent Lie groups
• Cartan connections and Kawaguchi geometry of spaces obtained by the moving frame method
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• Coherent states and geodesics: Cut locus and conjugate locus
• Coherent state representations. A survey
• Scalar curvature and projective embeddings. I
• Coherent state embeddings, polar divisors and Cauchy formulas
• On the existence of homogeneous geodesics in homogeneous Riemannian manifolds
• The Heisenberg group and the Riemannian contact manifolds
• Holomorphy and convexity in Lie theory
• Classifying 3 and 4 dimensional homogeneous Riemannian manifolds by Cartan triples
• Invariant metrics and Laplacians on Siegel-Jacobi disk
• Geometry of extended Bianchi-Cartan-Vranceanu spaces
• Coherent states, holomorphic extensions, and highest weight representations
• Parallel surfaces in the motion groups \(E(1,1)\) and \(E(2)\)
• On homogeneous Riemannian manifolds
• Einstein manifolds
• Invariant metrics and Laplacians on Siegel-Jacobi space
• Coherent states associated to the Jacobi group -- a variation on a theme by Erich Kähler
• Remarks on boson commutation rules
• Quaternion Riemann spaces with transitive reductive or solvable groups of motions
• Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization
• ON THE GEOMETRY OF SIEGEL–JACOBI DOMAINS
• A PARTIAL CAYLEY TRANSFORM OF SIEGEL-JACOBI DISK
• Survey on homogeneous geodesics
• The Sasakian Geometry of the Heisenberg Group
• Applications of the Jacobi group to Quantum Mechanics
• On the construction of perfect Morse functions on compact manifolds of coherent states
• A classification of coherent state representations of unimodular Lie groups
• Harmonic Analysis in Phase Space. (AM-122)
• On equations of motion on compact Hermitian symmetric spaces
• QUANTIZATION
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• COHERENT STATES AND KAHLER MANIFOLDS
• Naturally reductive metrics and Einstein metrics on compact Lie groups
• Linear dynamical systems, coherent state manifolds, flows, and matrix Riccati equation
• Legendre foliations on contact metric manifolds
• Mathematische Werke / Mathematical Works
• Quantization of Kahler Manifolds. II
• A CONVENIENT COORDINATIZATION OF SIEGEL–JACOBI DOMAINS
• CONSEQUENCES OF THE FUNDAMENTAL CONJECTURE FOR THE MOTION ON THE SIEGEL–JACOBI DISK
• Geometry and Arithmetic on the Siegel–Jacobi Space
• Coherent states and geometry on the Siegel–Jacobi disk
• A HOLOMORPHIC REPRESENTATION OF THE JACOBI ALGEBRA
• KÄHLERIAN MANIFOLDS ADMITTING A TRANSITIVE SOLVABLE AUTOMORPHISM GROUP
• The Automorphism Groups of Almost Hermitian Manifolds
• The action of a real semisimple group on a complex flag manifold. I: Orbit structure and holomorphic arc components
• Quantization and unitary representations
• Invariant Affine Connections on Homogeneous Spaces
• On the Theory of Automorphic Functions of a Matrix Variable I-Geometrical Basis
• Symplectic Geometry
• Elements of the representation theory of the Jacobi group
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The real Jacobi group revisited