TRANSVERSALLY BIHARMONIC MAPS BETWEEN FOLIATED RIEMANNIAN MANIFOLDS

Abstract

We generalize the notions of transversally harmonic maps between foliated Riemannian manifolds into transversally biharmonic maps. We show that a transversally biharmonic map into a foliated manifold of non-positive transverse curvature is transversally harmonic. Then we construct examples of transversally biharmonic non-harmonic maps into foliated manifolds of positive transverse curvature. We also prove that if f is a stable transversally biharmonic map into a foliated manifold of positive constant transverse sectional curvature and f satisfies the transverse conservation law, then f is a transversally harmonic map.