Riemannian Foliations and the Topology of Lorentzian Manifolds

Details Riemannian Foliations and the Topology of Lorentzian Manifolds Riemannian Foliations and the Topology of Lorentzian Manifolds

2010-10-11

arxiv.org/abs/1010.2194v1

Mathematics

Differential Geometry

16 pages, comments are welcome

Scientific paper

A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the (transverse) Ricci curvature is non-negative then a Bochner type argument implies that the first Betti number of $X$ is bounded by $1 \leq b_{1} \leq \dim X$ if $X$ is compact and $0 \leq b_{1} \leq \dim X -1$ otherwise. We show that these bounds are optimal and depending on the holonomy of $X$ we obtain further results. Finally, we classify the holonomy representations for those $X$ admitting a compact leaf with finite fundamental group.

Affiliated with

Also associated with

No associations

Rating

Riemannian Foliations and the Topology of Lorentzian 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 Riemannian Foliations and the Topology of Lorentzian Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Riemannian Foliations and the Topology of Lorentzian Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-659193