Elementary differential geometry. (©2006)

• Record Type: Book
• Further Information: Note: Barrett O'Neill.
• Other Names: O'Neill, Barrett
• Contents: Preface -- Introduction -- Chapter 1: Calculus on Euclidean Space: -- Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings. -- Chapter 2: Frame Fields: -- Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations. -- Chapter 3: Euclidean Geometry: -- Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves. -- Chapter 4: Calculus on a Surface: -- Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds. -- -- Chapter 5: Shape Operators: -- The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution. -- Chapter 6: Geometry of Surfaces in R3: -- The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces. -- Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet. -- Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard. -- Appendix -- Bibliography -- Answers to Odd-Numbered Exercises -- Subject Index.
• Edition: Rev. 2nd ed
• Publisher Details: Amsterdam Boston : Elsevier Academic Press
• Publication Date: 2006
• Copyright Date: 2006
• Extent: 1 online resource (xi, 503 pages), illustrations
• Subjects: 516.3/6; Geometry, Differential; Géométrie différentielle; MATHEMATICS -- Geometry -- Differential; Geometry, Differential; Geometria diferencial (textos elementares); Geometría diferencial; Géométrie différentielle; Surface (Mathématiques); Courbe; Differentialgeometrie; Electronic books
• Languages: English
• ISBNs: 9780080505428; 0080505422
• Related ISBNs: 0120887355; 9780120887354
• Notes: Note: Includes bibliographical references (page 467) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.