This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects. Discussions include submanifolds in Euclidean states and Riemannian space, minimal submanifolds, Grassman mappings, multi-dimensional regular polyhedra, and isometric immersions of Lobachevski space into Euclidean spaces. This volume also highlights the contributions made by great geometers to the geometry of submanifolds and its areas of application.
Curves. General Properties of Submanifolds. Hypersurface. Submanifolds in Euclidean States. Submanifolds in Riemannian Space. Two-Dimensional Surfaces in E4. Minimal Submanifolds. Grassman Image of a Submanifold. Regular Polyhedra in E4 and EN. Isometric Immersions of Lobachevski Space into Euclidean Spaces.