标题： 关于相对于超曲面的体积形式正规型定理的逆定理 显示英文标题

标题： A Converse to a Theorem on Normal Forms of Volume Forms with Respect to a Hypersurface

摘要： 在本文中，我们对 Y. Colin de Verdière 提出的一个问题给出了肯定回答，该问题涉及 A. N. Varchenko 所提出定理的逆定理：如果两个体积形式的芽相对于保持孤立超曲面奇点芽的微分同胚是等价的，且它们的差是某个形式的微分，该形式在超曲面的光滑部分的限制是恰当的，则成立。 显示英文摘要

摘要： In this note we give a positive answer to a question asked by Y. Colin de Verdi\`ere concerning the converse of the following theorem, due to A. N. Varchenko: two germs of volume forms are equivalent with respect to diffeomorphisms preserving a germ of an isolated hypersurface singularity, if their difference is the differential of a form whose restriction on the smooth part of the hypersurface is exact.