Article

Geometriae Dedicata

, Volume 53, Issue 1, pp 103-117

First online:

On completeness of certain families of semi-Riemannian manifolds

  • Alfonso RomeroAffiliated withDepartamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada
  • , Miguel SánchezAffiliated withDepartamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada

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Abstract

Semi-Riemannian manifolds with a suitable set of conformal symmetries are shown to be complete. Locally warped products are studied and warped-completeness is introduced. In the case of definite and complete basis, several assumptions on the growth of the warping function yield some of the three kinds of completeness. The case of 1-dimensional basis (including a known family of relativistic space-times) is specially studied. Null warped-completeness is related to the completeness of a certain conformal metric on the basis. Several examples and counter-examples explaining the main results are also given.

Mathematics Subject Classifications (1991)

53C22 53C50