Isometric embedding of the 2-sphere with non negative curvature in IR3.
We transform the problem of determining isometric immersions from into into that of solving equations of degenerate Monge-Ampère type on the unit ball . By presenting one family of special solutions to the equations, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
We characterize Clifford hypersurfaces and Cartan minimal hypersurfaces in a sphere by some properties of extrinsic shapes of their geodesics.