Intrinsicality of second fundamentals of hypersurfaces in space form

Pengfei Guan, Yu Yuan

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 $\ddot{I}{ƒ}_{2k+1}(A)\ne 0$ for some $k\g…