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Transversal wave maps and transversal exponential wave maps. (English) Zbl 1295.58007

A smooth mapping between Riemannian manifolds with Riemannian foliations is called transversally harmonic, if it is leaf-preserving and the trace of the transversal part of the second fundamental form vanishes. After basic facts about transversal harmonic maps established in [J. J. Konderak and R. A. Wolak, Q. J. Math. 54, No. 3, 335–354 (2003; Zbl 1059.53051)] and following papers, the authors of this paper generalize the concept, defining transversal wave maps and even transversal exponential wave maps, based on a functional involving \(\exp(|Df|^2)\) instead of \(|Df|^2\). Basic properties of those maps are proved, and the relations between the notions of wave maps, transversal wave maps, and transversal exponential wave maps are explored.

MSC:

58E20 Harmonic maps, etc.
58J45 Hyperbolic equations on manifolds
53C12 Foliations (differential geometric aspects)

Citations:

Zbl 1059.53051
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References:

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