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Local normal forms of singular Levi-flat hypersurfaces

Research paper by Arturo Fernández-Pérez, Gustavo Marra

Indexed on: 08 Oct '17Published on: 08 Oct '17Published in: arXiv - Mathematics - Complex Variables



Abstract

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.