关于广义Douglas-Weyl喷射的一个注记

A Note on Generalized Douglas-Weyl Spray

该文研究广义D ouglas-Weyl喷射.证明了一个喷射G是广义D ouglas-Weyl喷射当且仅当它的Weyl张量是二次型的.由此得到一个推论,一个芬斯勒度量是广义Douglas-Weyl度量当且仅当它的Weyl张量是二次型的.进一步,该文研究具有二次型的黎曼曲率张量的喷射,证明了一个喷射具有二次型的黎曼曲率张量当且仅当B_(j)^(i)_(kl)=0.

In this paper,we study Generalized Douglas-Weyl spray.We show that a spray G is a Generalized Douglas-Weyl spray if and only if it is W-quadratic.As a corollary,we show that a Finsler metric F is a Generalized Douglas-Weyl metric if and only if it is W-quadratic.Furthermore,we consider R-quadratic spray and prove that a spray G is R-quadratic if and only if B_(j)^(i)_(kl)=0.