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Harmonicity and minimality of distributions on Riemannian manifolds via the intrinsic torsion. (English) Zbl 1292.58009

The author shows that invariant Riemannian foliations of homogeneous Riemannian manifolds which are transversally symmetric determine harmonic maps and minimal immersions, and he provides many examples of harmonic maps and minimal immersions of compact Riemannian manifolds.

MSC:

58E20 Harmonic maps, etc.
53C30 Differential geometry of homogeneous manifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C10 \(G\)-structures
53C12 Foliations (differential geometric aspects)
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References:

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[10] González-Dávila, J. \? C. and Martín Cabrera, F.: Harmonic G-structures. Math. Proc. Cambridge Philos. Soc. 146 (2009), 435-459. · Zbl 1165.53043 · doi:10.1017/S0305004108001709
[11] González-Dávila, J. \? C. and Martín Cabrera, F.: Harmonic almost contact structures via the intrinsic torsion. Israel J. Math. 181 (2011), 145-187. · Zbl 1219.53075 · doi:10.1007/s11856-011-0007-7
[12] González-Dávila, J. \? C. and Martín Cabrera, F.: Homogeneous nearly Kähler manifolds. Ann. Glob. Anal. Geom. 42 (2012), 147-170. · Zbl 1258.53033 · doi:10.1007/s10455-011-9305-x
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