Book contents
- Frontmatter
- Contents
- The scope of this text
- Preface to the second edition
- Acknowledgments
- 1 How the theory of relativity came into being (a brief historical sketch)
- Part I Elements of differential geometry
- 2 A short sketch of 2-dimensional differential geometry
- 3 Tensors, tensor densities
- 4 Covariant derivatives
- 5 Parallel transport and geodesic lines
- 6 The curvature of a manifold; at manifolds
- 7 Riemannian geometry
- 8 Symmetries of Riemann spaces, invariance of tensors
- 9 Methods to calculate the curvature quickly: differential forms and algebraic computer programs
- 10 The spatially homogeneous Bianchi-type spacetimes
- 11 * The Petrov classication by the spinor method
- Part II The theory of gravitation
- References
- Index
2 - A short sketch of 2-dimensional differential geometry
from Part I - Elements of differential geometry
Published online by Cambridge University Press: 30 May 2024
Book contents
- Frontmatter
- Contents
- The scope of this text
- Preface to the second edition
- Acknowledgments
- 1 How the theory of relativity came into being (a brief historical sketch)
- Part I Elements of differential geometry
- 2 A short sketch of 2-dimensional differential geometry
- 3 Tensors, tensor densities
- 4 Covariant derivatives
- 5 Parallel transport and geodesic lines
- 6 The curvature of a manifold; at manifolds
- 7 Riemannian geometry
- 8 Symmetries of Riemann spaces, invariance of tensors
- 9 Methods to calculate the curvature quickly: differential forms and algebraic computer programs
- 10 The spatially homogeneous Bianchi-type spacetimes
- 11 * The Petrov classication by the spinor method
- Part II The theory of gravitation
- References
- Index
Summary
The need for differential geometry is explained by considering the construction of parallel straight lines running far from each other in Euclidean space. Generalisation of the notion of parallelism to curved surfaces is explained.
- Type
- Chapter
- Information
- An Introduction to General Relativity and Cosmology , pp. 9 - 11Publisher: Cambridge University PressPrint publication year: 2024