On transversally harmonic maps of foliated Riemannian manifolds

2011/09/19 by Jung, Min Joo, Jung, Seoung Dal
#53C #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.3932

Abstract

We study the transversally harmonic maps between foliated Riemannian manifolds. In particular, we prove that under some curvature conditions, any transversally harmonic map is transversally totally geodesic.

Related

• Harmonic maps on weighted Riemannian foliations
• Liouville type theorems for transversally harmonic and biharmonic maps
• A generalization of the Schwarz lemma for transversally harmonic maps
• Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold
• Liouville type theorem for (F;F')p-harmonic maps on foliations