General Relativity and Gravitation

, Volume 16, Issue 10, pp 921–942 | Cite as

Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions

  • G. E. Prince
  • M. Crampin
Research Articles


The Lagrangian structure of the geodesic equation allows an extension of classical projective geometry to one-parameter projective group actions onR×TM (whereM is the spacetime). We determine all those projective actions which arise by prolongation of oneparameter group actions onR×M. The relation between projective actions onR×TM and the equation of geodesic deviation is developed.


General Relativity Group Action Differential Geometry Projective Group Projective Action 
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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • G. E. Prince
    • 1
  • M. Crampin
    • 2
  1. 1.School of Theoretical PhysicsDublin Institute for Advanced StudiesDublin 4Ireland
  2. 2.Faculty of MathematicsThe Open University, Walton HallMilton KeynesUK

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