- #1
pmb_phy
- 2,952
- 1
Many times when I see the term Affine space used, the person using it seems to define it as a space with no origin or something akin to that. Its hard to find a definition of this term except the one that says an affine space is a space with is affinely connected where affinely connected is defined prier to this definition. MTW (page 242) use the the term affine geometry as that branch of mathematics which adds geodesics, parallel transport and curvature (shape) to a manifold. They then go on to say that that branch of mathematics which adds a metric is called Riemannian geometry.
I never could understand why people would think that an affine space is a space without an origin since the manifold on which the space is defined is simply a collection of points, anyone of which could be defined to be the origin of the manifold.
Could those who use the term "affine space" to mean a space without an origin please give me a reference to the source in which you found it defined like this? Thank you.
Best wishes
Pete
I never could understand why people would think that an affine space is a space without an origin since the manifold on which the space is defined is simply a collection of points, anyone of which could be defined to be the origin of the manifold.
Could those who use the term "affine space" to mean a space without an origin please give me a reference to the source in which you found it defined like this? Thank you.
Best wishes
Pete