Infinitesimal rigidity of hyperquadrics in semi-Euclidean space

In this paper, we show that hyperquadrics are infinitesimally rigid in a semi-Euclidean space. We also show that hypersurfaces of hyperquadrics cut by hyperplanes not passing through the origin are infinitesimally rigid in the hyperquadrics, whereas those cut by hyperplanes through the origin are not infinitesimally rigid in hyperquadrics. Furthermore, we prove that any hypersurface in a semi-Euclidean space containing some open subset of a hyperplane is not infinitesimally rigid.