Hokkaido Mathematical Journal

YOKUMOTO Ken,

On totally geodesic foliations perpendicular to Killing fields.

Hokkaido Mathematical Journal, 34 (2005) pp.679-688

Fulltext

PDF

Abstract

We study the codimension-one totally geodesic foliation perpendicular to a non-singular Killing field of a Lorentzian manifold. We determine the structure of the totally geodesic foliation perpendicular to a non-singular Killing field of a two-dimensional Lorentzian torus containing at least two kinds of leaves.

MSC(Primary)53C50
MSC(Secondary)57R30
Uncontrolled KeywordsLorentzian manifolds, totally geodesic foliations, Killing fields