论文标题
在高图和扭转歧义的变异定理上
On a variational theorem of Gauduchon and torsion-critical manifolds
论文作者
论文摘要
1984年，Gauduchon考虑了$ l^2 $ norm torsion $ 1 $ form的功能。他获得了此功能的Euler-Lagrange方程，并表明在尺寸$ 2 $中，关键指标必须保持平衡（即消失的Torsion $ 1 $ -FORM）。在本说明中，我们将其结果扩展到更高的维度，并表明关键指标在各个维度上都平衡。我们还考虑了整个Chern Torsion的$ l^2 $ norm，并以示例显示了该功能的关键点不是Kähler。
In 1984, Gauduchon considered the functional of $L^2$-norm of his torsion $1$-form on a compact Hermitian manifold. He obtained the Euler-Lagrange equation for this functional, and showed that in dimension $2$ the critical metrics must be balanced (namely with vanishing torsion $1$-form). In this note we extend his result to higher dimensions, and show that critical metrics are balanced in all dimensions. We also consider the $L^2$-norm of the full Chern torsion, and show by examples that there are critical points of this functional that are not Kähler.
