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Concepts from Tensor Analysis and Differential Geometry

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Author(s): Tracy Y. Thomas (Eds.)
Series: Mathematics in Science and Engineering 1
Publisher: AP
Year: 1961

Language: English
Commentary: no TOC
Pages: iii-v, 1-119

Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Page v
T.Y. Thomas

1. Coordinate Manifolds
Pages 1-5

2. Scalars
Page 6

3. Vectors and Tensors
Pages 7-12

4. A Special Skew-symmetric Tensor
Pages 13-15

5. The Vector Product. Curl of a Vector
Page 16

6. Riemann Spaces
Pages 17-28

7. Affinely Connected Spaces
Pages 29-31

8. Normal Coordinates
Pages 32-38

9. General Theory of Extension
Pages 39-44

10. Absolute Differentiation
Pages 45-47

11. Differential Invariants
Pages 48-53

12. Transformation Groups
Pages 54-56

13. Euclidean Metric Space
Pages 57-64

14. Homogeneous and Isotropic Tensors
Pages 65-69

15. Curves in Space. Frenet Formulae
Pages 70-74

16. Surfaces in Space
Pages 75-80

17. Mixed Surface and Space Tensors. Coordinate Extension and Absolute Differentiation
Pages 81-86

18. Formulae of Gauss and Weingarten
Pages 87-89

19. Gaussian and Mean Curvature of a Surface
Page 90

20. Equations of Gauss and Codazzi
Pages 91-92

21. Principal Curvatures and Principal Directions
Pages 93-98

22. Asymptotic Lines
Pages 99-100

23. Orthogonal Ennuples and Normal Congruences
Pages 101-107

24. Families of Parallel Surfaces
Pages 108-113

25. Developable Surfaces. Minimal Surfaces
Pages 114-115

Subject index
Pages 117-119