Tensor Valued Colombeau Functions on Manifolds ∗
نویسنده
چکیده
Extending the construction of the algebra Ĝ(M) of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M , via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension of the classical Lie derivative. Its members are smooth functions depending—via a third slot—on so-called transport operators, in addition to slots one (smooth n-forms on M) and two (points of M) from the scalar case. AMS Mathematics Subject Classification (2000): Primary 46F30; Secondary 46T30, 53A45.
منابع مشابه
Conformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
متن کاملRicci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
متن کاملThe Ultrarelativistic Reissner Nordstrrm Field in the Colombeau Algebra
The electromagnetic eld of the ultrarelativistic Reissner Nordstrrm Solution shows the physically highly unsatisfactory property of a vanishing eld tensor but a nonzero, i.e.-like, energy density. The aim of this work is to analyse this situation from a mathematical point of view, using the framework of Colombeau's theory of nonlinear generalized functions. It is shown that the physically unsat...
متن کاملNew ideas about multiplication of tensorial distributions
There is a huge need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept of Colombeau algebras, and the construction of full Colombeau algebras on differential manifolds for arbitrary tensors. Despite the fact that this goal ...
متن کاملOperator-valued tensors on manifolds
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
متن کامل