Inoguchi, Jun-ichi; Munteanu, Marian Ioan Magnetic maps. (English) Zbl 1317.53024 Int. J. Geom. Methods Mod. Phys. 11, No. 6, Article ID 1450058, 22 p. (2014). The authors introduce magnetic maps as critical points of the Landau-Hall integral and characterize them in terms of prescribed tension fields. Let \((N, h)\) and \((M, g)\) be two Riemannian manifolds and let \(f: (N, h)\longrightarrow (M, g)\) be a smooth map. Let \(\xi\) be a global vector field on \(N\) and \(\omega\) be a 1-form on \(M\). Then they prove that \(f\) is a magnetic map with respect to \(\xi\) and \(\omega\) if and only if it satisfies \[ \tau(f) = \phi(f_{*}\xi), \] where \(\tau(f)\) is the tension field of \(f\) and \(\omega\) is defined by \(g(\phi X, Y)= d\omega(X, Y)\), for all \(X\), \(Y\) tangent on \(M\). They provide some examples in Euclidean, contact and Kähler manifolds, and study some classes of magnetic surfaces in Euclidean 3-spaces. Reviewer: Fortuné Massamba (Pietermaritzburg) Cited in 6 Documents MSC: 53B25 Local submanifolds 53C22 Geodesics in global differential geometry 53C43 Differential geometric aspects of harmonic maps 53D25 Geodesic flows in symplectic geometry and contact geometry Keywords:magnetic curves; action integral; Landau Hall functional; harmonic maps; contact magnetic fields PDFBibTeX XMLCite \textit{J.-i. Inoguchi} and \textit{M. I. Munteanu}, Int. J. Geom. Methods Mod. Phys. 11, No. 6, Article ID 1450058, 22 p. (2014; Zbl 1317.53024) Full Text: DOI References: [1] DOI: 10.1016/j.difgeo.2011.04.001 · Zbl 1228.53050 · doi:10.1016/j.difgeo.2011.04.001 [2] DOI: 10.1063/1.2767535 · Zbl 1152.81329 · doi:10.1063/1.2767535 [3] DOI: 10.1063/1.2136215 · Zbl 1111.78006 · doi:10.1063/1.2136215 [4] Berndt J., J. Reine Angew Math. 395 pp 132– (1989) [5] Berndt J., Rend. Sem. Mat. Univ. Politec. Torino 55 pp 19– (1997) [6] DOI: 10.1007/978-1-4757-3604-5 · doi:10.1007/978-1-4757-3604-5 [7] DOI: 10.1017/S1446788700008715 · Zbl 1063.53069 · doi:10.1017/S1446788700008715 [8] DOI: 10.1007/s10474-009-9005-1 · Zbl 1212.53112 · doi:10.1007/s10474-009-9005-1 [9] DOI: 10.1088/1751-8113/42/19/195201 · Zbl 1188.78002 · doi:10.1088/1751-8113/42/19/195201 [10] Cecil T., Trans. Amer. Math. Soc. 269 pp 481– (1982) [11] DOI: 10.1016/0003-4916(87)90098-4 · Zbl 0635.58034 · doi:10.1016/0003-4916(87)90098-4 [12] DOI: 10.1063/1.3659498 · Zbl 1272.37020 · doi:10.1063/1.3659498 [13] DOI: 10.1112/blms/10.1.1 · Zbl 0401.58003 · doi:10.1112/blms/10.1.1 [14] DOI: 10.1090/cbms/050 · doi:10.1090/cbms/050 [15] DOI: 10.2748/tmj/1178241369 · Zbl 0261.53038 · doi:10.2748/tmj/1178241369 [16] Ikawa O., J. Geom. Symm. Phys. 4 pp 1– (2005) [17] DOI: 10.1090/S0002-9947-1986-0837803-2 · doi:10.1090/S0002-9947-1986-0837803-2 [18] DOI: 10.2307/1971420 · Zbl 0661.53027 · doi:10.2307/1971420 [19] DOI: 10.1016/j.geomphys.2011.10.002 · Zbl 1239.78003 · doi:10.1016/j.geomphys.2011.10.002 [20] DOI: 10.1070/RM1982v037n05ABEH004020 · Zbl 0571.58011 · doi:10.1070/RM1982v037n05ABEH004020 [21] DOI: 10.1063/1.4848775 · Zbl 1337.37056 · doi:10.1063/1.4848775 [22] Takagi R., Osaka J. Math. 10 pp 495– (1973) [23] DOI: 10.2969/jmsj/02710043 · Zbl 0292.53042 · doi:10.2969/jmsj/02710043 [24] DOI: 10.2969/jmsj/02740507 · Zbl 0311.53064 · doi:10.2969/jmsj/02740507 [25] DOI: 10.2996/kmj/1138845997 · Zbl 0188.26704 · doi:10.2996/kmj/1138845997 [26] Urakawa H., Translations of Mathematical Monographs 132, in: Calculus of Variations and Harmonic Maps (1993) [27] DOI: 10.2996/kmj/1138036191 · Zbl 0452.53034 · doi:10.2996/kmj/1138036191 [28] Zakrzewski W. J., Low-Dimensional Sigma Models (1989) · Zbl 0787.53072 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.