AIMS Mathematics, 2016, 1(1): 1-8. doi: 10.3934/Math.2016.1.1.

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Harmonic Maps Surfaces and Relativistic Strings

Department of Mathematics, University of Texas, Edinbrug, TX, 78540-2999, USA

The harmonic map is introduced and several physical applications are presented. The classical nonlinear σ model can be looked at as the embedding of a two-dimensional surface in a threedimensional sphere, which is itself embedded in a four-dimensional space. A system of nonlinear evolution equations are obtained by working out the zero curvature condition for the Gauss equations relevant to this geometric formulation.
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Keywords harmonic map; curvature; surface; soliton; sigma models

Citation: Paul Bracken. Harmonic Maps Surfaces and Relativistic Strings. AIMS Mathematics, 2016, 1(1): 1-8. doi: 10.3934/Math.2016.1.1


  • 1. P. Bracken, A. M. Grundland, On Certain Classes of Solutions of the Weierstrass-Enneper System Inducing Constant Mean Curvature Surfaces, J. Nonlin. Math. Phys. 6 (1999), 294-313.
  • 2. P.Bracken, A. M. Grundland, Properties and Explicit Solutions of the Generalized Weierstrass System, J. Math. Phys. 42 (2001), 1250-1282.
  • 3. S. Helgason, Di erential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
  • 4. F. Lund, T. Regge, Unified Approach to Strings and Vortices with Soliton Solutions, Phys. Rev. D, 14 (1976), 1524.
  • 5. F. Lund, Note on the Geometry of the Nonlinear σ Model in Two Dimensions, Phys. Rev. D, 15 (1977), 1540-1543.
  • 6. C. W. Misner, Harmonic maps as models for physical theories, Phys. Rev. D, 18 (1978), 4510-4524.
  • 7. K. Pohlmeyer, Integrable Hamiltonian Systems and Interactions through Quadratic Constraints, Commun. Math. Phys. 46 (1976), 207-221.


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