Minimal and Harmonic Unit Vector Fields in and Its Dual Space |
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Authors: | K Tsukada L Vanhecke |
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Institution: | (1) Ochanomizu University, Tokyo, Japan, JP;(2) Katholieke Universiteit Leuven, Belgium, BE |
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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 .
(Received 27 August 1999; in revised form 18 November 1999) |
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Keywords: | 1991 Mathematics Subject Classification: 53C20 53C25 53C35 53C40 53C42 53C55 58E20 |
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