Annali di Matematica Pura ed Applicata

, Volume 105, Issue 1, pp 121–139 | Cite as

Generic 2-surfaces and 2-2 foliations in general relativity

  • P. F. J. Dhooghe


Special points of spacelike and timelike 2-surfaces are defined by means of algebraic relations between the second order invariants of their immersion. Generic immersions are then defined and by means of direction fields constructed over the surface, the least number of such points is related to global properties of the surface. Moreover it is proved that every compact spacelike 2-surface has at least one point where the normal curvature is zero. Consequences are drawn for generic 2-spheres and trapped surfaces. The theorems are generalised to 2-2 foliations and fibrations.


General Relativity Special Point Global Property Direction Field Normal Curvature 
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© Fondazione Annali di Matematica Pura ed Applicata 1975

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  • P. F. J. Dhooghe

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