From PDE Systems and Metrics to Generalized Field Theories

Constantin Udriste; Mircea Neagu

From PDE Systems and Metrics to Generalized Field Theories

Differential Geometry 2010-07-30 v1 Analysis of PDEs

Authors: Constantin Udriste , Mircea Neagu

Abstract

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.

Keywords

bundle theory harmonic maps simplicial complexes

Cite

@article{arxiv.math/0101207,
  title  = {From PDE Systems and Metrics to Generalized Field Theories},
  author = {Constantin Udriste and Mircea Neagu},
  journal= {arXiv preprint arXiv:math/0101207},
  year   = {2010}
}

Comments

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

From PDE Systems and Metrics to Generalized Field Theories

Abstract

Keywords

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