  The Petrov type D equation imposed on the 2-metric tensor and the rotation
scalar of a cross-section of an isolated horizon can be used to uniquely
distinguish the Kerr - (anti) de Sitter spacetime in the case the topology of
the cross-section is that of a sphere. In the current paper we study that
equation on closed 2-dimensional surfaces that have genus $>0$. We derive all
the solutions assuming the embeddability in 4-dimensional spacetime that
satisfies the vacuum Einstein equations with (possibly 0) cosmological
constant. We prove all of them have constant Gauss curvature and zero rotation.
Consequently, we provide a quazi-local argument for a black hole in
4-dimensional spacetime to have a topologically spherical cross-section.
