标题： 在某些中性凯勒4流形中的面积平稳曲面 显示英文标题

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

摘要： 我们研究在TN中的曲面，这些曲面相对于从N上的黎曼度量g构造的中性凯勒度量是面积平稳的。我们证明TN中的全纯曲线是面积平稳的，而面积平稳的拉格朗日曲面也是全纯的，因此是完全零的。然而，一般来说，面积平稳的曲面不是全纯的。我们通过构造反例来证明这一点。在g具有旋转对称性的条件下，我们找到所有作为丛TN$\to$N的截面图的面积平稳曲面，并且这些曲面也具有旋转对称性。当(N,g)是圆球面时，TN可以与${\Bbb{R}}^3$中的定向仿射直线空间相联系，并且我们展示了一个两参数的面积平稳环面族，这些环面既不是全纯的也不是拉格朗日的。 显示英文摘要

摘要： 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$\to$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.