دانلود کتاب Lectures on Classical Differential Geometry: Second Edition

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Cover......Page 1
Title......Page 2
Copyright......Page 3
CONTENTS\0......Page 4
PREFACE\0......Page 6
BIBLIOGRAPHY\0......Page 8
1-1 Analytic representation\0......Page 12
1-2 Arc length, tangent\0......Page 16
1-3 Osculating plane\0......Page 21
1-4 Curvature\0......Page 24
1-5 Torsion\0......Page 26
1-6 Formulas of Frenet\0......Page 29
1-7 Contact\0......Page 34
1-8 Natural equations\0......Page 37
1-9 Helices\0......Page 44
1-10 General solution of the natural equations\0......Page 47
1-11 Evolutes and involutes\0......Page 50
1-12 Imaginary curves\0......Page 55
1-13 Ovals\0......Page 58
1-14 Monge\0......Page 64
2-1 Analytical representation\0......Page 66
2-2 First fundamental form\0......Page 69
2-3 Normal, tangent plane\0......Page 73
2-4 Developable surfaces\0......Page 77
2-5 Second fundamental form. Meusnier\'s theorem\0......Page 84
2-6 Euler\'s theorem\0......Page 88
2-7 Dupin\'s indicatrix\0......Page 94
2-8 Some surfaces\0......Page 97
2-9 A geometrical interpretation of asymptotic and curvature lines\0......Page 104
2-10 Conjugate directions\0......Page 107
2-11 Triply orthogonal systems of surfaces\0......Page 110
3-1 Gauss\0......Page 116
3-2 The equations of Gauss-Weingarten\0......Page 117
3-3 The theorem of Gauss and the equations of Codazzi\0......Page 121
3-4 Curvilinear coordinates in space\0......Page 126
3-5 Some applications of the Gauss and the Codazzi equations\0......Page 131
3-6 The fundamental theorem of surface theory\0......Page 135
4-1 Geodesic (tangential) curvature\0......Page 138
4-2 Geodesics\0......Page 142
4-3 Geodesic coordinates\0......Page 147
4-4 Geodesics as extremals of a variational problem\0......Page 151
4-5 Surfaces of constant curvature\0......Page 155
4-6 Rotation surfaces of constant curvature\0......Page 158
4-7 Non-Euclidean geometry\0......Page 161
4-8 The Gauss-Bonnet theorem\0......Page 164
5-1 Envelopes\0......Page 173
5-2 Conformal mapping\0......Page 179
5-3 Isometric and geodesic mapping\0......Page 186
5-4 Minimal surfaces\0......Page 193
5-5 Ruled surfaces\0......Page 200
5-6 Imaginaries in surface theory\0......Page 207
SOME PROBLEMS AND PROPOSITIONS\0......Page 212
APPENDIX: The method of Pfaffians in the theory of curves and surfaces.\0......Page 216
ANSWERS TO PROBLEMS\0......Page 228
INDEX\0......Page 237