Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)

One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.
The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.

• Riemannian Geometry
• Topology
• Principles of Mathematical Analysis
• Introduction to Differential Geometry of Space Curves and Surfaces: Differential Geometry of Curves and Surfaces
• Differential Geometry (Dover Books on Mathematics)
• Abstract Algebra
• Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)
• An Introduction to Manifolds: Second Edition (Universitext)
• Algebraic Topology
• Introduction to Topology: Third Edition (Dover Books on Mathematics)