Some comparisons of the Weyl conformal tensor and its classification in 4-dimensional Lorentz, neutral or positive definite signatures

摘要

This work is a study of the Weyl conformal tensor on manifolds of dimension 4 and for each of the three possible signatures (+,+,+,-), (+,+,-,-) and (+,+,+, +). In it, the properties of the Weyl tensor and its algebraic classification will be compared and contrasted.