ON TRANSVERSALLY HARMONIC MAPS OF FOLIATED RIEMANNIAN MANIFOLDS

Title & Authors
ON TRANSVERSALLY HARMONIC MAPS OF FOLIATED RIEMANNIAN MANIFOLDS
Jung, Min-Joo; Jung, Seoung-Dal;

Abstract
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 $\small{{\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})}$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then $\small{{\phi}}$ is transversally constant.
Keywords
transversal tension field;transversally harmonic map;normal variational formula;generalized Weitzenb$\small{\ddot{o}}$ck type formula;
Language
English
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2.
Harmonic Maps and Bi-Harmonic Maps on CR-Manifolds and Foliated Riemannian Manifolds, Journal of Applied Mathematics and Physics, 2016, 04, 12, 2272
3.
Variation formulas for transversally harmonic and biharmonic maps, Journal of Geometry and Physics, 2013, 70, 9
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