Invariant differential operators associated with a conformal metric
Invariant differential operators associated with a conformal metric
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DOI：
10.1307/mmj/1187647003
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发表时间：
2007-08
影响因子：
0.9
通讯作者：
Seong-A. Kim;T. Sugawa
中科院分区：
文献类型：
--
作者：
Seong-A. Kim;T. Sugawa
Peschl 定义了单位圆盘上全纯或亚纯函数的不变高阶导数。这里，不变性与源域的双曲度量和目标域的规范度量有关。 Minda 和 Schippers 将 Peschl 的不变导数扩展到一般共形度量的情况。我们为黎曼曲面上的平滑函数引入了类似的不变导数，并展示了 Faa di Bruno 的平滑函数与导数的全纯映射的合成公式的完整模拟。还将给出这些导数的内在几何和一些应用的解释。
Peschl defined invariant higher-order derivatives of a holomorphic or meromorphic function on the unit disk. Here, the invariance is concerned with the hyperbolic metric of the source domain and the canonical metric of the target domain. Minda and Schippers extended Peschl’s invariant derivatives to the case of general conformal metrics. We introduce similar invariant derivatives for smooth functions on a Riemann surface and show a complete analogue of Faa di Bruno’s formula for the composition of a smooth function with a holomorphic map with respect to the derivatives. An interpretation of these derivatives in terms of intrinsic geometry and some applications will be also given.