This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds are a classical subject in differential geometry. In fact, already in 1917 Cartan classified parametrically the Euclidean hypersurfaces that admit nontrivial conformal variations. Our first main result is a Fundamental theorem for conformal infinitesimal variations. The second is a rigidity theorem for Euclidean submanifolds that lie in low codimension.

中文翻译：

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子流形的共形无穷小变化

本文属于共形几何学领域，涉及欧几里得子流形，这些子流形允许无限变化的共形的平滑变化。欧几里得子流形的共形变化是微分几何学中的经典主题。实际上，在1917年，Cartan已经在参数上对欧几里得超曲面进行了分类，这些超曲面允许非平凡的共形变化。我们的第一个主要结果是共形无穷小变化的基本定理。第二个是位于低维数的欧几里得子流形的刚度定理。