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Transversally harmonic maps between manifolds with Riemannian foliations. (English) Zbl 1059.53051

Leaf preserving maps between manifolds with Riemannian foliations are considered and the transverse tension field for such maps is constructed. The authors introduce the notion of transversely harmonic maps and give a general characterization of these maps using the map induced on the level of transverse manifolds. They also prove that two foliated maps which induce isometrically equivalent maps on the level of transverse manifolds are transversely harmonic at the same time. In the end of the present paper some examples of transversely harmonic maps are given.

MSC:

53C43 Differential geometric aspects of harmonic maps
53C12 Foliations (differential geometric aspects)
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