论文标题
亚曼叶的完美无限变化
Conformal infinitesimal variations of submanifolds
论文作者
论文摘要
本文属于共形几何形状领域，并处理欧几里得的submanifolds，这些欧几里得submanifolds接受了无限同伴的光滑变化。欧几里得submanifolds的共形变化是差异几何学的经典主题。实际上，在1917年，卡坦已经从参数分类的是，欧几里得高度曲面接受了非平凡的保形变异。我们的第一个主要结果是用于完美无限变化的基本定理。第二个是欧几里得亚曼福尔德的刚度定理，位于较低的consimension中。
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 is 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.
