• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.977-991
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• 2012

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.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.593-610
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• 2023

In this paper, we prove the generalized Chen's conjecture for (𝓕, 𝓕')-biharmonic maps, such maps are critical points of the transversal bienergy functional.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.763-772
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• 2017

In this paper, we study the Liouville type theorems for transversally harmonic and biharmonic maps on foliated Riemannian manifolds.