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;