Representation theorems with variables in an intrinsic form
Abstract
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 Uα 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.
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