Holomorphically planar conformal vector fields on contact metric manifolds (Q626045)

The author studies holomorphically planar conformal vector fields \(V\) denoted by HPCV on: (i) contact metric manifolds with pointwise constant \(\xi\)-sectional curvature (then \(M\) is either \(K\)-contact or \(V\) is homothetic), (ii) Einstein contact metric manifolds (then \(M\) is \(K\)-contact), (b) contact metric manifolds with parallel Ricci tensor (then \(M\) is either \(K\)-contact Einstein or is locally isometric to \(E^{n+1}\times S^n(4)\)).