MG13 - Talk detail |
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Participant |
Beheshti, Shabnam | |||||||
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Institution |
Rutgers University - 110 Frelinghuysen Rd - Piscataway - NJ - USA | |||||||
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Session |
GT1 |
Accepted |
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Order |
Time |
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Talk |
Oral abstract |
Title |
Integrability & Vesture for Axially Symmetric Harmonic Maps | |||||
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Abstract |
We investigate the interrelationship between integrability, inverse-scattering (ISM), and vesture for harmonic maps into symmetric spaces. Motivated by the application of ISM to the Einstein Equations in the case of stationary, axisymmetric metrics, we show that the equations for an axially symmetric harmonic map of R^3 into a symmetric space G/K are completely integrable. Furthermore, new solutions for these equations can be generated starting from a given seed solution. As an application to General Relativity, we consider the problem of finding N-solitonic harmonic maps into the symmetric space SU(2,2) / S( U(2) x U(2) ) and find it is completely reducible via the vesture, or dressing, to a problem in linear algebra. Time permitting, we indicate directions for further investigation. |
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