The curvature tensor and the Einstein equations for a four-dimensional nonholonomic distribution

DOI10.3103/S1063454108030060zbMath1253.53045OpenAlexW2025367434WikidataQ125604391 ScholiaQ125604391MaRDI QIDQ1759540

V. R. Krym, N. N. Petrov

Publication date: 21 November 2012

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1063454108030060

zbMATH Keywords

variational principleDirac operatorelectromagnetic fieldcausal structure4-potential

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (25)

Graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Index form for nonholonomic distributions ⋮ Area formula for graph surfaces on five-dimensional sub-Lorentzian structures ⋮ Variations of nonholonomic-valued mappings and their applications to maximal surface theory ⋮ 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 ⋮ Maximal surfaces on five-dimensional group structures ⋮ Unnamed Item ⋮ 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 ⋮ 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 ⋮ Unnamed Item ⋮ Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ The Schouten curvature tensor and the Jacobi equation in sub-Riemannian geometry ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures ⋮ The Euler-Lagrange method in Pontryagin's formulation ⋮ Area of graph surfaces on Carnot groups with sub-Lorentzian structure ⋮ Nonholonomous geodesics as solutions to Euler-Lagrange integral equations and the differential of the exponential mapping ⋮ Graphs of nonsmooth contact mappings on Carnot groups with sub-Lorentzian structure

Cites Work

• On a generalization of Kaluza's theory of electricity
• On the existence of maximizing curves for the charged-particle action
• Quantised singularities in the electromagnetic field,
• The Large Scale Structure of Space-Time
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