On area-stationary surfaces in certain neutral Kaehler 4-manifolds

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dc.creatorGuilfoyle, Brendan
dc.creatorKlingenberg, Wilhelm
dc.date2006-11-22
dc.date.accessioned2026-07-07T10:19:15Z
dc.date.available2026-07-07T10:19:15Z
dc.descriptionWe study surfaces in TN that are area-stationary with respect to a neutral Kaehler metric constructed on TN from a riemannian metric g on N. We show that holomorphic curves in TN are area-stationary, while lagrangian surfaces that are area-stationary are also holomorphic and hence totally null. However, in general, area stationary surfaces are not holomorphic. We prove this by constructing counter-examples. In the case where g is rotationally symmetric, we find all area stationary surfaces that arise as graphs of sections of the bundle TN$\to$N and that are rotationally symmetric. When (N,g) is the round 2-sphere, TN can be identified with the space of oriented affine lines in ${\Bbb{R}}^3$, and we exhibit a two parameter family of area-stationary tori that are neither holomorphic nor lagrangian.
dc.description8 pages, AMS-LATEX, no figures
dc.identifierhttps://arxiv.org/abs/math/0611707
dc.identifierhttp://arxiv.org/abs/math/0611707
dc.identifierBeitraege Algebra Geom. 49 (2008) 481-490.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174444
dc.subjectDifferential Geometry
dc.subjectPrimary: 53B30; Secondary: 53A25
dc.titleOn area-stationary surfaces in certain neutral Kaehler 4-manifolds
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