Cartan联络及复〔α,β〕度量

The Cartan Connection and the Complex (α,β)-Metric

设F:T1,0M→R*为复流形M上的强凸复Finsler度量,一般的由F°诱导的Cartan联络及由F诱导的Chern-Finsler联络是不同的,主要在垂直丛上对这两种联络进行了比较;复α,β度量F=αφ(│β│/α)是较为重要的复Finsler度量,其中α2=aijdzidzj为M上的Hermitian度量,β=bizdzi为M上的1,0形式。计算了由F诱导的非线性联络系数Γ;αβ。

Assume that F：T^1,0M→R＊ is a strongly convex Finsler metric. In general the Cartan connection induce by F＊ and the Chern-Finsler connection induce by F might be different. This paper is devoted to compare them on the vertical bundle. The complex （ α,β ） -metric is very important in complex Finsler metrics, where α^2=αif dz^i dz^j is a Hermitian metric on M and β=bi（z）dz^i is a （1,0）-form on M. We calculate the explicit expression of the Christoffel symbols Гiβ^α of the complex non-linear connection associated to F.