1. On surfaces whose twistor lifts are harmonic sections
- Author
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Hasegawa, Kazuyuki
- Subjects
- *
VECTOR analysis , *CURVATURE , *CALCULUS , *DENSITY - Abstract
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. [Copyright &y& Elsevier]
- Published
- 2007
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