Homothetic maps of the space-time distance function and differentiability

Details Homothetic maps of the space-time distance function and differentiability Homothetic maps of the space-time distance function and differentiability

Sep 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978gregr...9..793b&link_type=abstract

General Relativity and Gravitation, Volume 9, Issue 9, pp.793-799

Physics

Scientific paper

Let (M 1,g 1) and (M 2,g 1) be time-oriented space-times. Letd i(p,q) be the supremum of lengths of future directed causal curves inM i fromp toq. Ifq is not in the future ofp, thend i (p, q)=0. A distance homothetic mapf is a function fromM 1 ontoM 2 which is not assumed to be continuous, but which satisfiesd 2(f(p),f(q))=cd 1(p,q) for allp,q ɛM 1. IfM 1 is strongly causal, then the distance homothetic mapf is a diffeomorphism which mapsg 1 to a scalar multiple ofg 2. Thus for strongly causal space-times, distance homothetic maps are homothetic in the usual sense. WhenM 1 is not strongly causal, distance homothetic maps are not necessarily differentiable nor even continuous. An example is given of a space-time which has discontinuous maps which are one to one, onto, and distance preserving.

Affiliated with

Also associated with

No associations

Rating

Homothetic maps of the space-time distance function and differentiability 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 Homothetic maps of the space-time distance function and differentiability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homothetic maps of the space-time distance function and differentiability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-941473