Related papers: Tensor Valued Colombeau Functions on Manifolds

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie…

Necessary and/or sufficient conditions are studied for the existence, uniqueness and holonomicity of bases in which on sufficiently general subsets of a differentiable manifold the components of derivations of the tensor algebra over it…

Let M be the interior of a compact 3-manifold with non-empty boundary, and T be an ideal (topological) triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi-angle structures…

Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…

We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…

It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…

This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

On a smooth manifold M, the Kashiwara index formula expresses the weighted Euler characteristic of a constructible function in terms of its characteristic cycle. We generalize this formula to the case when M is a smooth orbifold, answering…

Given a smooth toric variety $X$, the action of the torus $T$ lifts to the moduli space $\mathcal{M}$ of stable sheaves on $X$. Using the pioneering work of Klyacho, a fairly explicit combinatorial description of the fixed point locus…

Prescribed rational functions constitute a subset of rational functions satisfying certain symmetry and analyticity conditions. We define and construct explicitly prescribed rational functions-valued bundle $\mathcal{W}_M$ over a smooth…

Let $X=G/K$ be a symmetric space of the non-compact type. We prove that the mean value operator over translated $K$-orbits of a fixed point is surjective on the space of smooth functions on $X$ if $X$ is either complex or of rank one. For…

The Chekanov theorem generalizes the classic Lyusternik-Shnirel'man and Morse theorems concerning critical points of a smooth function on a closed manifold. A Legendrian submanifold \Lambda of space of 1-jets of the functions on a manifold…

In this paper we analyse the structure of the spaces of coefficients of eigenfunction expansions of functions in Komatsu classes on compact manifolds, continuing the research in our previous paper. We prove that such spaces of Fourier…

Fourth-order tensor-valued functions appear in numerous fields of study. The formulation of practical models for these complex functions often requires their representation in terms of tensors of order two. In this paper, we develop an…

Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…

We consider coefficient bodies $\mathcal M_n$ for univalent functions. Based on the L\"owner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a…

We present a definition of tensor fields which are average of tensors over a manifold, with a straightforward and natural definition of derivative for the averaged fields; which in turn makes a suitable and practical construction for the…

In this paper, we analyze the existing rules for constructing derivatives of the scalar and tensor functions of the tensor argument with respect to the tensor argument and the theoretical positions underlying the construction of these…

We introduce the new notion of convolution of a (smooth or generalized) valuation on a group $G$ and a valuation on a manifold $M$ acted upon by the group. In the case of a transitive group action, we prove that the spaces of smooth and…