Locally Convex Hypersurfaces of Negatively Curved Spaces
Locally Convex Hypersurfaces of Negatively Curved Spaces
A well-known theorem due to Hadamard states that if the second fundamental form of a compact immersed hypersurface M of Euclidean space ${E^n}(n \geqslant 3)$ is positive definite, then M is imbedded as the boundary of a convex body. There have been important generalizations of this theorem concerning hypersurfaces of …