From PDE Systems and Metrics to Generalized Field Theories

Details From PDE Systems and Metrics to Generalized Field Theories From PDE Systems and Metrics to Generalized Field Theories

2001-01-25

arxiv.org/abs/math/0101207v1

M. Neagu, C. Udriste: "From PDE systems and metrics to multi-time field theories and geometric dynamics", Seminarul de Mecanic

Mathematics

Differential Geometry

The authors express their sincere thanks to Professors V. Balan, V. Obadeanu and D. Opris for their critical reading of an ear

Scientific paper

The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are structured in the following way: 1) we find a suitable geometrical structure on $J^1(T,M)$ that convert the solutions of the given PDEs system into "generalized harmonic maps"; 2) we build a natural geometry induced by a such PDEs system; 3) we construct a field theory, in a general setting, naturally attached to this PDEs system.

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