论文标题
Kähler形式和曲率的耦合方程的矩图
Moment map for coupled equations of Kähler forms and curvature
论文作者
论文摘要
在本文中，我们介绍了Kähler几何形状中的两个新方程系统：耦合P方程和广义耦合的CSCK方程。我们激发了从映射图片的时刻来激励方程，证明了解决方案的独特性，并找出了第二个方程的解决方案的障碍。我们还指出了耦合的CSCK方程，耦合的KählerYang-Mills方程与变形的Hermitian Yang-Mills方程之间的连接。 此外，使用此瞬间图，我们可以显示用于广义耦合CSCK方程的mabuchi函数，以及耦合的KählerYang-Mills方程的特殊情况，而沿平滑的大地测量的耦合KählerYang-Mills方程和变形的Hermitian Yang-Mills方程是沿平滑的convex conconvex的，这与矩图组不同。在我们的情况下，大地测量是由自然度量给出的，对光滑的kähler势$ \ mathcal {k}（x，x，ω_0）\ times \ cdots \ cdots \ times \ times \ times \ mathcal {k}（x，ω_k）$。
In this paper we introduce two new systems of equations in Kähler geometry: The coupled p equation and the generalized coupled cscK equation. We motivate the equations from the moment map pictures, prove the uniqueness of solutions and find out the obstructions to the solutions for the second equation. We also point out the connections between the coupled cscK equation, the coupled Kähler Yang-Mills equations and the deformed Hermitian Yang-Mills equation. Moreover, using this moment map, we can show the Mabuchi functional for the generalized coupled cscK equation, and a special case of the coupled Kähler Yang-Mills equations and the deformed Hermitian Yang-Mills equation are convex along the smooth geodesic, which is different from the one using the moment map picture from the gauge group. In our case, the geodesic is given by the natural metric on the product of smooth Kähler potential $\mathcal{K}(X,ω_0)\times \cdots \times \mathcal{K}(X,ω_k)$.
