  We study normal forms of germs of singular real-analytic Levi-flat
hypersurfaces. We prove the existence of rigid normal forms for singular
Levi-flat hypersurfaces which are defined by the vanishing of the real part of
complex quasi-homogeneous polynomials with isolated singularity. This result
generalizes previous results of Burns-Gong and Fern\'andez-P\'erez.
Furthermore, we prove the existence of two new rigid normal forms for singular
real-analytic Levi-flat hypersurfaces which are preserved by a change of
isochore coordinates, that is, a change of coordinates that preserves volume.
