Home on Jonathan Bergknoff · Jan 17, 2014

Wald GR, Chapter 3 Notes

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3.0: Curvature Extrinsic curvature of a manifold is a notion of curvature relying on embedding the manifold in a higher-dimensional space. It will be discussed in chapter 9.
Intrinsic curvature of a manifold, with no reference to a higher-dimensional space, can be defined in terms of parallel transport.
Parallel transport is roughly “to keep a tangent vector pointing in the same…

3.0: Curvature Extrinsic curvature of a manifold is a notion of curvature relying on embedding the manifold in a higher-dimensional space. It will be discussed in chapter 9. Intrinsic curvature of a manifold, with no reference to a higher-dimensional space, can be defined in terms of parallel transport. Parallel transport is roughly “to keep a tangent vector pointing in the same direction” as it is moved around the manifold (across the various different tangent spaces).

Read on /journal/gr/wald-3/ ↗

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