Local Rigidity of Hyperspaces in Real Euclidean Spaces
Chung-Ki Cho, Chong-Kyu Han · Rocky Mountain Journal of Mathematics · 2000
This paper studies the rigidity of isometric immersions of n-dimensional Riemannian manifolds into the (n + 1)-dimensional Euclidean space.In the formalism of jet theory for partial differential equations, we investigate the relationship between the rigidity of immersions and the existence of complete systems of order 2. We define the notion of jet-rigidity as an intrinsic concept of a Riemannian structure and show that nondegenerate isometric immersions of jet-rigid Riemannian manifolds are actually rigid.We also get another proof of the classical Beez-Killing theorem on the rigidity of hypersurfaces.