Cartan's Structural Equations for Degenerate Metric

Mathematics – Differential Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. On singular semi-Riemannian manifolds, because the metric is allowed to be degenerate, there are some obstructions in constructing the geometric objects normally associated to the metric. We can no longer construct local orthonormal frames and coframes, or define a metric connection and its curvature operator. But we will see that if the metric is radical stationary, we can construct objects similar to the connection and curvature forms of Cartan, to which they reduce if the metric is non-degenerate. We write analogs of Cartan's first and second structural equations. As a byproduct we will find a compact version of the Koszul formula.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Cartan's Structural Equations for Degenerate Metric 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 Cartan's Structural Equations for Degenerate Metric, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cartan's Structural Equations for Degenerate Metric will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-700349

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.