Harmonic Maps Surfaces and Relativistic Strings
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/10.3934/Math.2016.1.1/fulltext.html |
| _version_ | 1818057276118794240 |
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| author | Paul Bracken |
| author_facet | Paul Bracken |
| author_sort | Paul Bracken |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T12:42:09Z |
| format | Article |
| id | doaj.art-4073fc7c11f24e518c21defa806f05a6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T12:42:09Z |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-4073fc7c11f24e518c21defa806f05a62022-12-22T01:48:29ZengAIMS PressAIMS Mathematics2473-69882016-04-01111810.3934/Math.2016.1.1Harmonic Maps Surfaces and Relativistic StringsPaul Bracken0Department of Mathematics, University of Texas, Edinbrug, TX, 78540-2999, USAThe 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.http://www.aimspress.com/article/10.3934/Math.2016.1.1/fulltext.htmlharmonic map| curvature| surface| soliton| sigma models |
| spellingShingle | Paul Bracken Harmonic Maps Surfaces and Relativistic Strings AIMS Mathematics harmonic map| curvature| surface| soliton| sigma models |
| title | Harmonic Maps Surfaces and Relativistic Strings |
| title_full | Harmonic Maps Surfaces and Relativistic Strings |
| title_fullStr | Harmonic Maps Surfaces and Relativistic Strings |
| title_full_unstemmed | Harmonic Maps Surfaces and Relativistic Strings |
| title_short | Harmonic Maps Surfaces and Relativistic Strings |
| title_sort | harmonic maps surfaces and relativistic strings |
| topic | harmonic map| curvature| surface| soliton| sigma models |
| url | http://www.aimspress.com/article/10.3934/Math.2016.1.1/fulltext.html |
| work_keys_str_mv | AT paulbracken harmonicmapssurfacesandrelativisticstrings |