Book contents
- Frontmatter
- Contents
- List of figures
- The scope of this text
- Acknowledgements
- 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; flat manifolds
- 7 Riemannian geometry
- 8 Symmetries of Riemann spaces, invariance of tensors
- 9 Methods to calculate the curvature quickly – Cartan forms and algebraic computer programs
- 10 The spatially homogeneous Bianchi type spacetimes
- 11 * The Petrov classification by the spinor method
- Part II The theory of gravitation
- References
- Index
6 - The curvature of a manifold; flat manifolds
Published online by Cambridge University Press: 01 March 2010
Book contents
- Frontmatter
- Contents
- List of figures
- The scope of this text
- Acknowledgements
- 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; flat manifolds
- 7 Riemannian geometry
- 8 Symmetries of Riemann spaces, invariance of tensors
- 9 Methods to calculate the curvature quickly – Cartan forms and algebraic computer programs
- 10 The spatially homogeneous Bianchi type spacetimes
- 11 * The Petrov classification by the spinor method
- Part II The theory of gravitation
- References
- Index
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- An Introduction to General Relativity and Cosmology , pp. 36 - 47Publisher: Cambridge University PressPrint publication year: 2006