A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary

Details A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary

2011-04-18

arxiv.org/abs/1104.3378v1

Journal of Geometry and Physics, Vol. 61, No. 5. (07 May 2011), pp. 927-939

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages

Scientific paper

10.1016/j.geomphys.2010.12.013

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the `edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this `edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use.

Affiliated with

Also associated with

No associations

Rating

A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-71407