ISSN:
1436-5081
Keywords:
1991 Mathematics Subject Classification: 53C20
;
53C25
;
53C35
;
53C40
;
53C42
;
53C55
;
58E20
;
Key words: Minimal and harmonic unit vector fields
;
harmonic maps
;
the complex two-plane Grassmannian and its dual space
;
special classes of real hypersurfaces
;
tubes
;
radial vector fields
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. The complex two-plane Grassmannian carries a Kähler structure J and also a quaternionic Kähler 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 .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00010086
Permalink