Given a Hörmander system on a domain we show that any subelliptic harmonic morphism from into a -dimensional riemannian manifold is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also is a submersion provided that and has rank . If (the Heisenberg group) and , where is the Lewy operator, then a smooth map is a subelliptic harmonic morphism if and only if is a harmonic morphism, where is the canonical circle bundle and is the Fefferman metric of . For any -invariant weak solution to the harmonic map equation on the corresponding base map is shown to be a weak subelliptic harmonic map. We obtain a regularity result for weak harmonic morphisms from into a riemannian manifold, where is the Fefferman metric associated to the system of vector fields on .
@article{ASNSP_2003_5_2_2_379_0, author = {Barletta, Elisabetta}, title = {H\"ormander systems and harmonic morphisms}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {379--394}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {2}, year = {2003}, mrnumber = {2005608}, zbl = {1170.58305}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_2_379_0/} }
TY - JOUR AU - Barletta, Elisabetta TI - Hörmander systems and harmonic morphisms JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 379 EP - 394 VL - 2 IS - 2 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_2_379_0/ LA - en ID - ASNSP_2003_5_2_2_379_0 ER -
Barletta, Elisabetta. Hörmander systems and harmonic morphisms. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 2, pp. 379-394. http://www.numdam.org/item/ASNSP_2003_5_2_2_379_0/
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