  It has been known that warped product spacetimes such as spherically
symmetric ones admit the Kodama vector. This vector provides a locally
conserved current made by contraction of the Einstein tensor, even though there
is no Killing vector. In addition, a quasilocal mass, Birkhoff's theorem and
various properties are closely related to the Kodama vector. Recently, it is
shown that the notion of the Kodama vector can be extended to three-dimensional
axisymmetric spacetimes even if the spacetimes are not warped product. This
implies that warped product may not be a necessary condition for a spacetime to
admit the Kodama vector. We show properties of the Kodama vector originate from
the conformal Killing-Yano two-form. In particular, the well-known spacetimes
that admit the Kodama vector have a closed conformal Killing-Yano two-form.
Furthermore, we show the Kodama vector provides local conserved currents for
each order of the Lovelock tensor as well as the Einstein tensor.
