  The intrinsic geometry of the Kerr ergosurface on constant Boyer-Lindquist
(BL), Kerr, and Doran time slices is characterized. Unlike the BL slice, which
had been previously studied, the other slices (i) do not have conical
singularities at the poles (except the Doran slice in the extremal limit), (ii)
have finite polar circumference in the extremal limit, and (iii) for
sufficiently large spin parameter fail to be isometrically embeddable as a
surface of revolution above some latitude. The Doran slice develops an
embeddable polar cap for spin parameters greater than about 0.96.
