ON TRANSVERSALLY HARMONIC MAPS OF FOLIATED RIEMANNIAN MANIFOLDS Jung, Min-Joo; Jung, Seoung-Dal;
Let (M,F) and (M`,F`) be two foliated Riemannian manifolds with M compact. If the transversal Ricci curvature of F is nonnegative and the transversal sectional curvature of F` is nonpositive, then any transversally harmonic map is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then is transversally constant.
transversal tension field;transversally harmonic map;normal variational formula;generalized Weitzenbck type formula;