Intrinsicality of second fundamentals of hypersurfaces in space form

Abstract

We prove that the normalized second fundamental form $A$ of immersed $C^2$ hypersurface in a space form $(N^{n+1},\bar{g})$ is intrinsic provided ${\sigma }_{2k+1}(A)\ne 0$ for some $k\ge 1$. We also establish the intrinsicality of the normalized second fundamental form $A$ of $M^n=\partial \Omega$ for domain $\Omega \subset N^{n+1},n\ge 3$.