| 000 | 02425cam a2200229 a 4500 | ||
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| 999 |
_c256 _d256 |
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| 001 | 834 | ||
| 005 | 20200611103823.0 | ||
| 008 | 051202s2006 ne a b 001 0 eng | ||
| 020 | _a0120887355 (acidfree paper) | ||
| 020 | _a9780120887354 (hbk) | ||
| 040 | _cDLC | ||
| 082 | 0 | 0 |
_a516.36 _222 _bN411 |
| 100 | 1 | _aO'Neill, Barrett. | |
| 245 | 1 | 0 |
_aElementary differential geometry / _cBarrett O'Neill. |
| 250 | _aRev. 2nd ed. | ||
| 260 |
_aAmsterdam : _aBoston : _bElsevier Academic Press, _cc2006. |
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| 300 |
_axi, 503 p. _bill. ; _c24 cm. |
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| 500 | _aIncludes bibliographical references (p. 467) and index. | ||
| 650 | 0 | _aGeometry, Differential. | |
| 942 | _cBK | ||
| 505 | 0 | _aIntroduction 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 | |