Semi-C-Reducible Conformally Doubly Warped Product Finsler Metric

设F1和F2分别是光滑流形M1和M2上的芬斯勒度量，共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒度量是类C2芬斯勒度量。Let F1 and F2 be two Finsler metrics on smooth manifold M1 and M2,respectively.The conformally doubly warped product Finsler metric F2=e2σ(f22F12+f12F22) is a Finsler metric endowed on the M=M1×M2 ,where f1、f2 and σ are positive smooth functions on M1 、M2 and M, respectively.It is proved that semi-C-reducible conformally doubly warped product Finsler metric is a C2-like Finsler metric.