Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators

Details Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators

2008-11-24

arxiv.org/abs/0811.3841v1

Mathematics

Differential Geometry

Scientific paper

We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic (resp. C-k for finite k at least 2) pseudo-Riemannian metric on M defined near P. We construct a torsion free real analytic (resp. C-k) connection D which is defined near P on the tangent bundle of M whose curvature operator is the given operator R at P and so that D has constant scalar curvature. We show that if R is Ricci symmetric, then D can be chosen to be Ricci symmetric; if R has trace free Ricci tensor, then D can be chosen to have trace free Ricci tensor; if R is Ricci alternating, then D can be chosen to be Ricci alternating.

Affiliated with

Also associated with

No associations

Rating

Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators 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 Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-645041