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Full-Text Articles in Physical Sciences and Mathematics
On Area-Stationary Surfaces In Certain Neutral Kaehler 4-Manifolds, Brendan Guilfoyle, Wilhelm Klingenberg
On Area-Stationary Surfaces In Certain Neutral Kaehler 4-Manifolds, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
We 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→N and that are rotationally symmetric. When (N,g) is the round 2-sphere, TN can be …
On Hamilton’S Characteristic Functions For Reflection, Brendan Guilfoyle, Wilhelm Klingenberg
On Hamilton’S Characteristic Functions For Reflection, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
We review the complex differential geometry of the space of oriented affine lines in R3 and give a description of Hamilton’s characteristic functions for reflection in an oriented C1 surface in terms of this geometry.