论文标题
伪里曼尼亚语歧管之间地图的第二基本形式的整体不变的变异问题
Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds
论文作者
论文摘要
我们研究了整体不变的变异问题，这些问题被定义为第二基本形式的不变函数的整合，在伪里曼尼亚歧管之间平滑地图。我们得出了由二维的不变均匀多项式定义的整体不变式的第一个变异公式。在这些积分不变的人中，我们表明Chern-Federer Energy功能的Euler-Lagrange方程将降低为二阶PDE。然后，我们为Riemannian空间形式提供了一些Chern-Federer Submanifolds的例子。
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae for integral invariants defined from invariant homogeneous polynomials of degree two. Among these integral invariants, we show that the Euler-Lagrange equation of the Chern-Federer energy functional is reduced to a second order PDE. Then we give some examples of Chern-Federer submanifolds in Riemannian space forms.
