Stability of twistor lifts for surfaces in four-dimensional manifolds as harmonic sections

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Hasegawa, Kazuyuki¹ 

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, Tokyo 1628601, Japan

关键词: Twistor space;    Twistor lift;    Twistor holomorphic surface;    Self-dual Einstein manifold;    Vertical energy;    Harmonic section;   

DOI  :  10.1016/j.geomphys.2009.06.014

来源: Elsevier

【 摘 要 】

We prove that the twistor lifts of certain twistor holomorphic surfaces in four-dimensional manifolds are weakly stable harmonic sections. As a corollary, if ambient spaces are self-dual Einstein manifolds with nonnegative scalar curvature, then the twistor lifts of twistor holomorphic surfaces are weakly stable. Moreover, for certain surfaces in four-dimensional hyperkahler manifolds. we show that the surfaces are twistor holomorphic if their twistor lifts are weakly stable harmonic sections. In particular, we characterize twistor holomorphic surfaces in four-dimensional Euclidean space by weak stability of the twistor lifts. (c) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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