Proof of the Carathéodory Conjecture by Mean Curvature Flow in the Space of Oriented Affine Lines Brendan Guilfoyle and Wilhelm Klingenberg
نویسنده
چکیده
منابع مشابه
Geodesic Flow on Global Holomorphic Sections of Ts Brendan Guilfoyle and Wilhelm Klingenberg
We study the geodesic flow on the global holomorphic sections of the bundle π : TS → S induced by the neutral Kähler metric on the space of oriented lines of R, which we identify with TS. This flow is shown to be completely integrable when the sections are symplectic and the behaviour of the geodesics is described.
متن کاملGeodesic Flow on the Normal Congruence of a Minimal Surface Brendan Guilfoyle and Wilhelm Klingenberg
We study the geodesic flow on the normal line congruence of a minimal surface in R induced by the neutral Kähler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in R and relate it to the classical Weierstrass representation.
متن کاملArea-stationary Surfaces in Neutral Kähler 4-Manifolds
We study surfaces in TN that are area-stationary 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 counter-examples. In the case where g is rotationally symmetric, we find all area-stationary surfaces ...
متن کاملar X iv : m at h / 04 05 18 9 v 1 [ m at h . D G ] 1 1 M ay 2 00 4 ON THE SPACE OF ORIENTED AFFINE LINES IN R 3
We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean R 3 and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces in R 3 , as we illustrate with a number of explicit examples. The correspondence between oriented affine lines in R 3 and the tangent bundle to the 2-sphere has a lon...
متن کاملOn Area-stationary Surfaces in Certain Neutral Kähler 4-manifolds Brendan Guilfoyle and Wilhelm Klingenberg
We study surfaces in TN that are area-stationary 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 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 count...
متن کامل