We investigate Kähler metrics conformal to gradient Ricci solitons, and base
metrics of warped product gradient Ricci solitons. A slight generalization
of the latter we name quasi-solitons. A main assumption that is employed
is functional dependence of the soliton potential, with the conformal
factor in the first case, and with the warping function in the second.
The main result in the first case is a partial classification in dimension
. In
the second case, Kähler quasi-soliton metrics satisfying the above main assumption
are shown to be, under an additional genericity hypothesis, necessarily Riemannian
products. Another theorem concerns quasi-soliton metrics satisfying the above main
assumption, which are also conformally Kähler. With some additional assumptions
it is shown that such metrics are necessarily base metrics of Einstein warped
products, that is, quasi-Einstein.
