We study holomorphically planar conformal vector fields (HPCV) on contact metric manifolds under some curvature conditions. In particular, we have studied HPCV fields on (i) contact metric manifolds with pointwise constant ξ-sectional curvature (under this condition M is either K-contact or V is homothetic), (ii) Einstein contact metric manifolds (in this case M becomes K contact), (iii) contact metric manifolds with parallel Ricci tensor (under this condition M is either K-contact Einstein or is locally isometric to E n+1×S n (4)).
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机译：我们研究了在某些曲率条件下接触度量流形上的全纯平面共形矢量场（HPCV）。尤其是，我们研究了（i）具有点向恒定ξ截面曲率的接触度量歧管（在这种情况下M为K接触或V为同质），（ii）爱因斯坦接触度量歧管（在这种情况下为M变为K接触），（iii）具有平行Ricci张量的接触度量歧管（在这种情况下，M是K接触爱因斯坦或与E n + 1 ×S n局部等距的（4））。
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