Summary
By interpreting the σ-nonlinear model as describing the Gauss map associated to a certain immersion, several classes of classical solutions for the 4-dimensional model are derived. As by-products one points out i) an intimate connection between the energy-momentum tensor of the solution and the second differential form of the immersion associated to it and ii) a connection between self- (antiself-)duality of the solution and the minimality of the associated immersion.
Riassunto
Interpretando il modello con σ non lineare come un modello che descrive la mappatura di Gauss associata ad una certa immersione, si derivano parecchie classi di soluzioni classiche per il modello a quattro dimensioni. Come sottoprodotti si segnalano i) una connessione stretta tra il tensore energia-impulso della soluzione e la forma differenziale seconda dell'immersione ad essa associata e ii) una connessione tra auto (antiauto) dualità della soluzione e la minimalità dell'immersione associata.
Резюме
Интерпретируя нелинейную σ-модель как модель, описывающую гауссово отображение, связанное с иммерсией, выводятся несколько классов классических решений для четырехмерной модели. Отмечается: 1) тесная связь между тензором энергии-импульса для решения и выражением для иммерсии в виде дифференциалов второго порядка; 2) связь между само- (анти-само-)-дуальностью решения и минимальностью ассоциированной иммерсии.
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Tataru-Mihai, P. Classical solutions for the 4-dimensional σ-nonlinear model. Nuov Cim A 51, 169–179 (1979). https://doi.org/10.1007/BF02775418
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DOI: https://doi.org/10.1007/BF02775418