Minimal and Harmonic Unit Vector Fields in and Its Dual Space |
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Authors: | K. Tsukada and L. Vanhecke |
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Affiliation: | (1) School of Mathematics, Trinity College Dublin, Dublin 2, Ireland;(2) Department of Mathematics, University of York, Heslington, York, Y010 5DD, UK |
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Abstract: | The complex two-plane Grassmannian carries a K?hler structure J and also a quaternionic K?hler structure ?. For we consider the classes of connected real hypersurfaces (M, g) with normal bundle such that and are invariant under the action of the shape operator. We prove that the corresponding unit Hopf vector fields on these hypersurfaces always define minimal immersions of (M, g), and harmonic maps from (M, g), into the unit tangent sphere bundle with Sasaki metric . The radial unit vector fields corresponding to the tubular hypersurfaces are also minimal and harmonic. Similar results hold for the dual space . |
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