## Differential Geometry of Curves and Surfaces: Revised and Updated Second EditionOne 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. |

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#### Review: Differential Geometry of Curves and Surfaces

User Review - Mark Hoyle - GoodreadsExcellent treatise on curves and surfaces with very clear exposition of the motivation behind many concepts in Riemannian Geometry. Read full review

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angle appendix to Chap arc length arcwise connected Assume asymptotic curves axis closed curve coefficients compact complete surface compute condition conjugate const constant contained contradiction convex coordinate curves coordinate neighborhood cylinder defined definition denote diffeomorphism differentiable function differentiable map ds ds equations Example Exercise exists a neighborhood fact Figure follows Gauss Gauss map Gaussian curvature geodesic given hence homeomorphism intersection isometry Jacobi field Lemma local isometry mean curvature normal vector obtain open set orthogonal parallel transport parametrized by arc parametrized curve parametrized surface plane curve proof Prop PROPOSITION prove regular curve regular parametrized regular surface Remark restriction ruled surface Show surface of revolution tangent plane tangent vector theorem U C R unit vector vector field zero