Includes bibliographical references (pages 355-365) and indexes.
1. Curves -- 2. General Properties of Submanifolds -- 3. Hypersurfaces -- 4. Submanifolds in Euclidean Space -- 5. Submanifolds in Riemannian Space -- 6. Two-Dimensional Surfaces in E[superscript 4] -- 7. Minimal Submanifolds -- 8. Grassmann Image of a Submanifold -- 9. Regular Polyhedra in E[superscript 4] and E[superscript N] -- 10. Isometric Immersions of Lobachevski Space into Euclidean Space.
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"This volume provides a comprehensive presentation of the geometry of submanifolds and expands classical results in the theory of curves and surfaces. The geometry of submanifolds begins 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 local and global aspects. The volume also highlights the contributions made by great geometers, past and present, to the geometry of submanifolds and the developing areas of application."--Jacket.