منابع مشابه
The Prolongation Formula for Tensor Fields
We derive a generalization of the prolongation formula for tensorvalued functions, by taking into account the natural action of di eomorphisms on tensor elds. This di ers from the usual procedure, where such elds are viewed as de ning \multi-component scalars;" it replaces the ordinary derivative in the expression of the \characteristic" by a Lie derivative. The resulting version of Noether's t...
متن کاملThe Formula of Grangeat for Tensor Fields of Arbitrary Order in n Dimensions
The cone beam transform of a tensor field of order m in n >/= 2 dimensions is considered. We prove that the image of a tensor field under this transform is related to a derivative of the n-dimensional Radon transform applied to a projection of the tensor field. Actually the relation we show reduces for m = 0 and n = 3 to the well-known formula of Grangeat. In that sense, the paper contains a ge...
متن کاملRevisiting Brauer’s formula for tensor product decompositions
The notation used here will be explained below. A familiar (though oversimplified) example is given for the Lie algebra sl2(C) by the Clebsch– Gordan formula; as in [2, Exer. 22.7]. In 1937 Richard Brauer published a short note giving a general formula of this sort. It still serves as the starting point for some computer methods, even though it usually involves a large number of cancellations. ...
متن کاملLagrangian Formalism for Tensor Fields
The Lagrangian formalism for tensor fields over differentiable manifolds with different (not only by sign) contravariant and covariant affine connections and a metric [(Ln, g)-spaces] is considered. The functional variation and the Lie variation of a Lagrangian density, depending on components of tensor fields (with finite rank) and their first and second covariant derivatives are established. ...
متن کاملAn Index Formula for Loewner Vector Fields
Let f be C2 real-valued function defined near 0 in R2, ∂2f ∂z2 6= 0 for z 6= 0. Motivated by the Carathéodory conjecture in differential geometry, Loewner conjectured that the index at 0 of the vector field given in complex notation by ∂ 2f ∂z2 is at most two. In this paper we establish a formula that computes the index of these Loewner vector fields from data about the hessian of f .
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1994
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/27/23/029