On the Weyl tensor of a self-dual complex 4-manifold

Details On the Weyl tensor of a self-dual complex 4-manifold On the Weyl tensor of a self-dual complex 4-manifold

2000-02-04

arxiv.org/abs/math/0002029v1

Mathematics

Differential Geometry

42 pages, 18 figures

Scientific paper

We study complex 4-manifolds with holomorphic self-dual conformal structures, and we obtain an interpretation of the Weyl tensor of such a manifold as the projective curvature of a field of cones on the ambitwistor space. In particular, its vanishing is implied by the existence of some compact, simply-connected, null-geodesics. We also relate the Cotton-York tensor of an umbilic hypersurface to the Weyl tensor of the ambient. As a consequence, a conformal 3-manifold or a self-dual 4-manifold admitting a rational curve as a null-geodesic is conformally flat. We show that the projective structure of the beta-surfaces of a self-dual manifold is flat.

Affiliated with

Also associated with

No associations

Rating

On the Weyl tensor of a self-dual complex 4-manifold 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 On the Weyl tensor of a self-dual complex 4-manifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Weyl tensor of a self-dual complex 4-manifold will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233072