论文标题
在$ u（n）$ - 不变的强烈凸复杂的Finsler指标
On $U(n)$-invariant strongly convex complex Finsler metrics
论文作者
论文摘要
在本文中，我们获得了$ u（n）$ - 不变的复杂的复杂的鳍状量$ f $ $ \ mathbb {c}^n $的必要条件，以强烈凸出，这也可以通过混凝土和可计算示例研究真实和复杂的Finsler几何形式之间的关系。我们证明了一个僵化的定理，该定理指出，当$ f $来自$ u（n）$ u（n）$ - 不变的Hermitian Metric时，强烈凸出的Finsler Metric $ f $ a $ u（n）$ - 不变的finsler metric $ f $。我们给出了$ u（n）$ - 不变的弱复杂的Berwald指标，具有消失的全体形态截面曲率，并获得了$ u（n）$的全体形态曲率的明确公式 - 不变的强烈pseudoconvex finsler finsler finsler finsler量表。最后，我们证明了一些$ u（n）$ - 不变的复杂的鳍度量的真正的测量学限制了单位球体$ \ pmb {s}^{2n-1} \ subset \ subset \ subset \ mathbb {c}^n $共享特定的特定属性，因为该属性是$ \ mathbb {c}^n $的$ \ mathbb {c}^n $的特定属性。
In this paper, we obtain a necessary and sufficient condition for a $U(n)$-invariant complex Finsler metric $F$ on domains in $\mathbb{C}^n$ to be strongly convex, which also makes it possible to investigate relationship between real and complex Finsler geometry via concrete and computable examples. We prove a rigid theorem which states that a $U(n)$-invariant strongly convex complex Finsler metric $F$ is a real Berwald metric if and only if $F$ comes from a $U(n)$-invariant Hermitian metric. We give a characterization of $U(n)$-invariant weakly complex Berwald metrics with vanishing holomorphic sectional curvature and obtain an explicit formula for holomorphic curvature of $U(n)$-invariant strongly pseudoconvex complex Finsler metric. Finally, we prove that the real geodesics of some $U(n)$-invariant complex Finsler metric restricted on the unit sphere $\pmb{S}^{2n-1}\subset\mathbb{C}^n$ share a specific property as that of the complex Wrona metric on $\mathbb{C}^n$.cc
