Projectively Osserman manifolds

Details Projectively Osserman manifolds Projectively Osserman manifolds

2007-08-09

arxiv.org/abs/0708.1210v1

Mathematics

Differential Geometry

Scientific paper

One says that a smooth manifold M is a pseudo-Riemannian manifold of signature (p,q) if the tangent bundle TM is equipped with a smooth non-degenerate symmetric inner product g of signature (p,q). Similarly one says that M is an affine manifold if TM is equipped with a torsion free connection. One says g is Osserman if the eigenvalues of the Jacobi operator are constant on the pseudo-sphere bundles of unit timelike and spacelike vectors. We extend this concept from the pseudo-Riemannian to the affine setting to define the notion of a projectively Osserman manifold. This notion is the focus of the paper. We establish some basic results concerning projectively Osserman manifolds and exhibit examples of this structure which arise in several different geometrical contexts.

Affiliated with

Also associated with

No associations

Rating

Projectively Osserman manifolds 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 Projectively Osserman manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projectively Osserman manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-417067