Journal of the
Korean Mathematical Society JKMS

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p\in M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of $T_pM$, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

Keywords: Einstein space, warped product, conformal vector field

MSC numbers: 53C50, 53A30, 53C25