Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894509 | Journal of Geometry and Physics | 2007 | 18 Pages |
Abstract
We study surfaces whose twistor lifts are harmonic sections, and characterize these surfaces in terms of their second fundamental forms. As a corollary, under certain assumptions for the curvature tensor, we prove that the twistor lift is a harmonic section if and only if the mean curvature vector field is a holomorphic section of the normal bundle. For surfaces in four-dimensional Euclidean space, a lower bound for the vertical energy of the twistor lifts is given. Moreover, under a certain assumption involving the mean curvature vector field, we characterize a surface in four-dimensional Euclidean space in such a way that the twistor lift is a harmonic section, and its vertical energy density is constant.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Kazuyuki Hasegawa,