论流形边界上具有奇点的列维平坦超曲面

Pub Date : 2024-07-15 DOI:10.1002/mana.202300343

Arturo Fernández-Pérez, Gustavo Marra

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引用次数: 0

摘要

我们研究边界流形上具有奇点的实解析李维平超曲面的胚芽。我们证明了实解析李维平超曲面的正常形式的存在，该形式由、、和奇点的实部消失所定义。最后，我们证明了边界上有奇点的实解析李维平超曲面的莫尔斯-韦伊(Morse-Vey) Lemma。

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On Levi-flat hypersurfaces with singularities on a manifold boundary

We study germs of real-analytic Levi-flat hypersurfaces with singularities on a boundary manifold. We prove the existence of a normal form for a real-analytic Levi-flat hypersurface which is defined by the vanishing of the real part of $B_{k}$ , $C_{k}$ , and $F_{4}$ singularities. Finally, we prove a version of Morse–Vey's lemma for a real-analytic Levi-flat hypersurface with singularities on the boundary.

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