Geometric analysis on quaternion \(\mathbb H\)-type groups

DOI10.1007/BF02922116zbMath1093.53042OpenAlexW2116314144MaRDI QIDQ819255

Irina Markina, Der-Chen E. Chang

Publication date: 28 March 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922116

zbMATH Keywords

Hamiltonian formalismquaternionsnilpotent Lie groupsCarnot-Carathéodory metrics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Sub-Riemannian geometry (53C17) Subelliptic equations (35H20)

Related Items (17)

Sub-Riemannian geodesics and heat operator on odd dimensional spheres ⋮ On the homomorphisms of the Lie groups \(\mathrm{SU}(2)\) and \(S^3\) ⋮ Geodesics on \({\mathbb{H}}\)-type quaternion groups with sub-Lorentzian metric and their physical interpretation ⋮ Sub-semi-Riemannian geometry of general \(H\)-type groups ⋮ The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group ⋮ Sub-Riemannian geometry of parallelizable spheres ⋮ Wavelet transform and Radon transform on the quaternion Heisenberg group ⋮ Quaternion \(H\)-type group and differential operator \(\Delta_\lambda \) ⋮ Anisotropic quaternion Carnot groups: Geometric analysis and Green function ⋮ Pseudo-metric 2-step nilpotent Lie algebras ⋮ Geometric analysis on quaternion anisotropic Carnot groups ⋮ Geometric analysis on H -type groups related to division algebras ⋮ On octonionic regular functions and the Szegő projection on the octonionic Heisenberg group ⋮ Weyl transform and generalized spectrogram associated with quaternion Heisenberg group ⋮ The heat kernel and Green functions of sub-Laplacians on the quaternion Heisenberg group ⋮ Nonholonomic Lorentzian geometry on some \(\mathbb H\)-type groups ⋮ On the tangential Cauchy-Fueter operators on nondegenerate quadratic hypersurfaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {H}^2}$\end{document}

Cites Work

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• On the Geometry of Groups of Heisenberg Type
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• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
• Rigidity of \(H\)-type groups

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