Differential Geometry in Physics (Lecture Notes)

✍ Scribed by Gabrile Lugo

• Publisher: Gabrile Lugo
• Year: 2006
• Tongue: English
• Leaves: 61
• Category: Library

✦ Table of Contents

Preface......Page 4
Contents......Page 6
1.1 Tangent Vectors......Page 7
R3......Page 9
1.3 Fundamental Theorem of Curves......Page 18
2.1 1-Forms......Page 21
2.2 Tensors and Forms of Higher Rank......Page 23
2.3 Exterior Derivatives......Page 29
2.4 The Hodge- Operator......Page 31
3.1 Frames......Page 39
3.2 Curvilinear Coordinates......Page 41
3.3 Covariant Derivative......Page 44
3.4 Cartan Equations......Page 46
4.1 Manifolds......Page 49
4.2 The First Fundamental Form......Page 50
4.3 The Second Fundamental Form......Page 54
4.4 Curvature......Page 57