论文标题
在Kähler潜力空间中行动最少的原则
The principle of least action in the space of Kähler potentials
论文作者
论文摘要
鉴于紧凑的Kähler歧管，其（相对）Kähler势的空间$ \ Mathcal H $是无限的尺寸Fréchet歧管，Mabuchi和Semmes在其上引入了自然连接$ \ nabla $。我们在$ t \ Mathcal H $（尤其是Finsler指标）上研究某些Lagrangians，与该连接相关。我们表明，$ \ nabla $的大地测量是行动最少的路径。在适当的条件下，匡威也保持；并证明动作最少的一定凸性属性。这概括了卡拉比，陈和达瓦斯的早期结果。
Given a compact Kähler manifold, the space $\mathcal H$ of its (relative) Kähler potentials is an infinite dimensional Fréchet manifold, on which Mabuchi and Semmes have introduced a natural connection $\nabla$. We study certain Lagrangians on $T\mathcal H$, in particular Finsler metrics, that are parallel with respect to the connection. We show that geodesics of $\nabla$ are paths of least action; under suitable conditions the converse also holds; and prove a certain convexity property of the least action. This generalizes earlier results of Calabi, Chen, and Darvas.
