Abstracto
- Let M be a differentiable manifold of dimension 3 with a Riemannian metric, not necessarily positive definite. In an open neighborhood of each point of M we can find three (real, differentiable) vector fields, ∂ a , which form an orthonormal rigid triad, that is, at each point of their domain of definition, the vector fields ∂ a form an orthonormal basis of the tangent space to M at that point. In order to make use of the results of the preceding chapter, we shall assume that the (constant) components of the metric with respect to the basis {∂1, ∂2, ∂3} are given by (g ab ) = diag(l, 1, 1) or by (g ab ) = diag(l, 1,−1).