Differential Geometry of Three Dimensions: Volume 2

Originally published in 1930, as the second of a two-part set, this textbook contains a vectorial treatment of geometry.

C. E. Weatherburn (Author)

9781316606957, Cambridge University Press

Paperback / softback, published 15 April 2016

252 pages
21.6 x 14 x 1.5 cm, 0.33 kg

Originally published in 1930, as the second of a two-part set, this informative and systematically organized textbook, primarily aimed at university students, contains a vectorial treatment of geometry, reasoning that by the use of such vector methods, geometry is able to be both simplified and condensed. Topics covered include Flexion and Applicability of Surfaces, Levi-Civita's theory of parallel displacements on a surface and the theory of Curvilinear Congruences. Diagrams are included to supplement the text. Providing a detailed overview of the subject and forming a solid foundation for study of multidimensional differential geometry and the tensor calculus, this book will prove an invaluable reference work to scholars of mathematics as well as to anyone with an interest in the history of education.

Preface
1. Differential invariants for a surface
2. Families of curves on a surface
3. Families of curves (continued)
4. Ruled surfaces. Weingarten surfaces
5. Curvilinear coordinates in space. Differential invariants
6. Families of surfaces
7. Tensors of the second order
8. Families of curves and functions of direction on a surface
9. Levi-Civita's parallel displacements. Tchebychef systems
10. Representation of surfaces. Conical projection
11. Small deformations of curves and surfaces
12. Flexion of surfaces. Applicability
13. Curvilinear congruences
Index.

Subject Areas: Geometry [PBM]