Heinrich W Guggenheimer

Differential Geometry

• Broschiertes Buch

Produktbeschreibung

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Produktdetails

• Verlag: Dover Publications
• Seitenzahl: 400
• Erscheinungstermin: 1. Juni 1977
• Englisch
• Abmessung: 209mm x 143mm x 20mm
• Gewicht: 422g
• ISBN-13: 9780486634333
• ISBN-10: 0486634337
• Artikelnr.: 21898455

Inhaltsangabe

Preface Chapter 1. Elementary Differential Geometry 1
1 Curves 1
2 Vector and Matrix Functions 1
3 Some Formulas Chapter 2. Curvature 2
1 Arc Length 2
2 The Moving Frame 2
3 The Circle of Curvature Chapter 3. Evolutes and Involutes 3
1 The Riemann
Stieltjès Integral 3
2 Involutes and Evolutes 3
3 Spiral Arcs 3
4 Congruence and Homothety 3
5 The Moving Plane Chapter 4. Calculus of Variations 4
1 Euler Equations 4
2 The Isoperimetric Problem Chapter 5. Introduction to Transformation Groups 5
1 Translations and Rotations 5
2 Affine Transformations Chapter 6. Lie Group Germs 6
1 Lie Group Germs and Lie Algebras 6
2 The Adjoint Representation 6
3 One
parameter Subgroups Chapter 7. Transformation Groups 7
1 Transformation Groups 7
2 Invariants 7
3 Affine Differential Geometry Chapter 8. Space Curves 8
1 Space Curves in Euclidean Geometry 8
2 Ruled Surfaces 8
3 Space Curves in Affine Geometry Chapter 9. Tensors 9
1 Dual Spaces 9
2 The Tensor Product 9
3 Exterior Calculus 9
4 Manifolds and Tensor Fields Chapter 10. Surfaces 10
1 Curvatures 10
2 Examples 10
3 Integration Theory 10
4 Mappings and Deformations 10
5 Closed Surfaces 10
6 Line Congruences Chapter 11. Inner Geometry of Surfaces 11
1 Geodesics 11
2 Clifford
Klein Surfaces 11
3 The Bonnet Formula Chapter 12. Affine Geometry of Surfaces 12
1 Frenet Formulas 12
2 Special Surfaces 12
3 Curves on a Surface Chapter 13. Riemannian Geometry 13
1 Parallelism and Curvature 13
2 Geodesics 13
3 Subspaces 13
4 Groups of Motions 13
5 Integral Theorems Chapter 14. Connections Answers to Selected Exercises Index