Geodesic
Symmetries, conservation laws, and exact solutions in nonlinear sigma models
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 1, pp. 45-54

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Nonlinear four-dimensional $\sigma$ models interacting with the gravitational field are considered. On the basis of the connection between the groups of isometric motions of the space-time $V_4$ and the space $V_N$ of values of the chiral field exact solutions are obtained for the Einstein and chiral-field equations for spherical and plane symmetry. The conserved currents associated with the presence of the isometric motions in $V_N$ are constructed. 
@article{TMF_1983_57_1_a5,
     author = {G. G. Ivanov},
     title = {Symmetries, conservation laws, and exact solutions in nonlinear sigma models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_57_1_a5/}
}
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G. G. Ivanov. Symmetries, conservation laws, and exact solutions in nonlinear sigma models. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 1, pp. 45-54. http://geodesic.mathdoc.fr/item/TMF_1983_57_1_a5/