Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics

Details Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics

2009-04-03

arxiv.org/abs/0904.0535v1

Trans. Amer. Math. Soc. 363 (2011), 4081-4107

Mathematics

Differential Geometry

39 pages, no pictures

Scientific paper

Two metrics $g $ and $\bar g$ are geodesically equivalent, if they share the same (unparameterized) geodesics. We introduce two constructions that allow one to reduce many natural problems related to geodesically equivalent metrics, such as the classification of local normal forms and the Lie problem (the description of projective vector fields), to the case when the (1,1)-tensor $G^i_j:= g^{ik} \bar g_{kj}$ has one real eigenvalue, or two complex conjugate eigenvalues, and give first applications. As a part of the proof of the main result, we generalize Topalov-Sinjukov (hierarchy) Theorem for pseudo-Riemannian metrics

Affiliated with

Also associated with

No associations

Rating

Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics 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 Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-150597