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Space-time decompositions via differential forms. (English) Zbl 0948.83006
Slovák, Jan (ed.) et al., Proceedings of the 17th winter school “Geometry and physics”, Srní, Czech Republic, January 11-18, 1997. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 54, 33-43 (1998).
The author presents a simple method (by using the standard theory of connections on principle bundles) of \((3+1)\)-decomposition of the physical equations written in terms of differential forms on a 4-dimensional spacetime of general relativity, with respect to a general observer. Finally, the author suggests possible applications of such a decomposition to the Maxwell theory.
For the entire collection see [Zbl 0904.00040].
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
58A10 Differential forms in global analysis