JP Journal of Geometry and Topology
Volume 13, Issue 1, Pages 93 - 117
(February 2013)
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TRANSVERSALLY f-HARMONIC AND TRANSVERSALLY f-BIHARMONIC MAPS BETWEEN FOLIATED MANIFOLDS
Yuan-Jen Chiang and Robert A. Wolak
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Abstract: Transversally f-harmonic maps between foliated Riemannian manifolds generalize transversally harmonic maps [22, 23]. Transversally f-harmonic maps and f-harmonic maps are different. However, if y is an f-harmonic map under certain circumstance, then it is a transversally f-harmonic map. We also investigate transversally f-biharmonic maps, which generalize transversally biharmonic maps [10]. We show that if y is a transversally f-biharmonic map from a compact foliated manifold into a foliated manifold with non-positive transverse curvature satisfying a condition, then it is a transversally f‑harmonic map. |
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