Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 481490 (2008) 

Areastationary surfaces in neutral Kähler 4manifoldsBrendan Guilfoyle and Wilhelm KlingenbergDepartment of Mathematics and Computing, Institute of Technology, Tralee Clash, Tralee, Co. Kerry, Ireland, email: brendan.guilfoyle@ittralee.ie, Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom, email: wilhelm.klingenberg@@durham.ac.ukAbstract: We study surfaces in TN that are areastationary with respect to a neutral Kähler metric constructed on TN from a Riemannian metric g on N. We show that holomorphic curves in TN are areastationary. However, in general, area stationary surfaces are not holomorphic. We prove this by constructing counterexamples. In the case where g is rotationally symmetric, we find all area stationary surfaces that arise as graphs of sections of the bundle TN$\rightarrow$N and that are rotationally symmetric. When (N,g) is the round 2sphere, TN can be identified with the space of oriented affine lines in ${\Bbb{R}}^3$, and we exhibit a two parameter family of areastationary tori that are neither holomorphic nor Lagrangian. Keywords: maximal surface, mean curvature, neutral Kähler Classification (MSC2000): 53B30; 53A25 Full text of the article:
Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.
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