Determination of the metric from the connection

Details Determination of the metric from the connection Determination of the metric from the connection

2006-09-26

arxiv.org/abs/math-ph/0609075v3

Physics

Mathematical Physics

21 pages

Scientific paper

As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its Levi-Civita connection? It is shown that for a generic Levi-Civita connection of a metric $h$ there exists a set of positive semi-definite tensor fields $h_{a}$ such that the parallel metrics are the positive-definite linear combinations of the $h_{a}$. Moreover, the set of all parallel metrics may be constructed by a soley algebraic procedure.

Affiliated with

Also associated with

No associations

Rating

Determination of the metric from the connection 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 Determination of the metric from the connection, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determination of the metric from the connection will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-261283