Representation theorems with variables in an intrinsic form

  • Sebastiano Pennisi


In a Minkowski space V, consideration is given to the tensor-valued isotropic functions of an arbitrary number of tensors of which one is a time-like vector and another is a symmetric tensor Aαβ,  such that Âαβ, its space-space part orthogonal to Uα, has distinct eigenvalues.

Representations are given for these functions in terms of an orthonormal basis of eigenvectors UA α of  Âαβ (A=0,1,2,3). The relationship between the total and the partial derivative of these function with respect to the independent components of UA α  is also obtained in covariant form.