Geodesics on \({\mathbb{H}}\)-type quaternion groups with sub-Lorentzian metric and their physical interpretation

DOI10.1007/s11785-010-0079-0zbMath1201.53037arXiv1004.1508OpenAlexW2144147683WikidataQ126019990 ScholiaQ126019990MaRDI QIDQ601083

Anna Korolko, Irina Markina

Publication date: 3 November 2010

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.1508

zbMATH Keywords

electromagnetic fieldspecial relativitysub-Lorentzian metricquaternion H-type group

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Sub-Riemannian geometry (53C17)

Related Items (22)

Graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Area formula for graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Surface area on two-step sub-Lorentzian structures with multi-dimensional time ⋮ The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure ⋮ Fundamental solutions of a class of ultra-hyperbolic operators on pseudo \(H\)-type groups ⋮ Remarks on global sub-Lorentzian geometry ⋮ Sub-semi-Riemannian geometry of general \(H\)-type groups ⋮ Sub-Lorentzian coarea formula for mappings of Carnot groups ⋮ The area of graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ Two-step sub-Lorentzian structures and graph surfaces ⋮ Measure of images of contact mappings on two-step sub-Lorentzian structures ⋮ Classes of maximal surfaces on Carnot groups ⋮ The area of graphs on arbitrary Carnot groups with sub-Lorentzian structure ⋮ Maximal Surfaces on Two-Step Sub-Lorentzian Structures ⋮ Coarea formula for functions on 2-step Carnot groups with sub-Lorentzian structure ⋮ Space-likeness of classes of level surfaces on Carnot groups and their metric properties ⋮ Graphs of Lipschitz mappings on two-step sub-Lorentzian structures with multidimensional time ⋮ Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures ⋮ Area of graph surfaces on Carnot groups with sub-Lorentzian structure ⋮ Graphs of nonsmooth contact mappings on Carnot groups with sub-Lorentzian structure ⋮ On the approximability and parametrization of preimages of elements of Carnot groups on sub-Lorentzian structures

Cites Work

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• Semi-Riemannian geometry with nonholonomic constraints
• Geometric analysis on quaternion \(\mathbb H\)-type groups
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Reachable sets for the Heisenberg sub-Lorentzian structure on \(\mathbb R^3\). An estimate for the distance function
• Sub-Lorentzian geometry on anti-de Sitter space
• Nonholonomic Lorentzian geometry on some \(\mathbb H\)-type groups
• Normal forms of germs of contact sub-Lorentzian structures on \(\mathbb R^3\). Differentiability of the sub-Lorentzian distance function
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• The geometry of Minkowski spacetime. An introduction to the mathematics of the special theory of relativity

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