Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON TRANSVERSALLY HARMONIC MAPS OF FOLIATED RIEMANNIAN MANIFOLDS

  • Jung, Min-Joo (Department of Mathematics Jeju National University) ;
  • Jung, Seoung-Dal (Department of Mathematics and Research Institute for Basic Sciences Jeju National University)
  • Received : 2011.01.20
  • Published : 2012.09.01
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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 ${\phi}:(M,F){\rightarrow}(M^{\prime},F^{\prime})$ is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ${\phi}$ is transversally constant.

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References

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