广义(α,β)-度量的共形向量场

On Conformal Vector Fields of General(α,β)-metrics

本文主要研究了广义(α,β)-度量的共形向量场.我们在关于Φ的一定条件下刻画了广义(α,β)-度量的共形向量场.作为一个重要应用,当α具有常数截面曲率且β是关于α的共形1-形式时,我们完全决定了(α,β)-度量的共形向量场.

In this paper,we mainly study conformal vector fields of general(a,β)-metrics.We characterize the conformal vector fields of general(α,β)-metrics with certain conditions aboutΦ.As a natural application,we completely determine conformal vector fields of(α,β)-metrics whenαhas constant sectional curvature andβis a conformal 1-form with respect toα.