General Relativity and Gravitation

, Volume 27, Issue 3, pp 319–339

Slicing, threading and parametric manifolds

  • Stuart Boersma
  • Tevian Dray

DOI: 10.1007/BF02109128

Cite this article as:
Boersma, S. & Dray, T. Gen Relat Gravit (1995) 27: 319. doi:10.1007/BF02109128


We present a unified treatment of theslicing (3+1) andthreading (1+3) decompositions of spacetime in terms of foliations. It is well-known how to decompose the metric and connection in the slicing picture; this is at the heart of any initial-value problem in general relativity. We describe here the analogous problem in the threading picture, recovering the recent results of Perjés onparametric manifolds.

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Stuart Boersma
    • 1
  • Tevian Dray
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA
  2. 2.Division of Mathematics and Computer ScienceAlfred UniversityAlfredUSA