Tensor valued Colombeau functions on manifolds

M. Grosser

Displaying similar documents to “Tensor valued Colombeau functions on manifolds”

On torsion of a $3$ -web

Alena Vanžurová (1995)

Mathematica Bohemica

Similarity:

A 3-web on a smooth $2 n$ -dimensional manifold can be regarded locally as a triple of integrable $n$ -distributions which are pairwise complementary, [5]; that is, we can work on the tangent bundle only. This approach enables us to describe a $3$ -web and its properties by invariant $(1, 1)$ -tensor fields $P$ and $B$ where $P$ is a projector and $B^{2} =$ id. The canonical Chern connection of a web-manifold can be introduced using this tensor fields, [1]. Our aim is to express the torsion tensor $T$ of the Chern connection...

Coincidence of topologies on tensor products of Köthe echelon spaces

J. Bonet, A. Defant, A. Peris, M. Ramanujan (1994)

Studia Mathematica

Similarity:

We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from $l_{p}$ to $l_{q}$ . Several sharp forms of this result are also included.

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

Similarity:

The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.

On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol (2007)

Studia Mathematica

Similarity:

For a (DF)-space E and a tensor norm α we investigate the derivatives $T o r_{α}^{l} (E, \cdot)$ of the tensor product functor $E \otimes ̃_{α} \cdot : \to$ from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of $T o r ¹_{α} (E, F)$ , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

Equivalences involving (p,q)-multi-norms

Oscar Blasco, H. G. Dales, Hung Le Pham (2014)

Studia Mathematica

Similarity:

We consider (p,q)-multi-norms and standard t-multi-norms based on Banach spaces of the form $L^{r} (Ω)$ , and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the [p,q]-concave multi-norm, and relate it to the standard t-multi-norm.

Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

Similarity:

We study whether the operator space $V * * \overset{α}{\otimes} W * *$ can be identified with a subspace of the bidual space $(V \overset{α}{\otimes} W) * *$ , for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be...

Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)

Christian Brouder, Nguyen Viet Dang, Frédéric Hélein (2016)

Studia Mathematica

Similarity:

The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front sets satisfy some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces $_{Γ}^{'}$ of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is not continuous for the usual topology on $_{Γ}^{'}$ , and the tensor product is not separately continuous....

Conformal Ricci Soliton in Lorentzian $α$ -Sasakian Manifolds

Tamalika Dutta, Nirabhra Basu, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian $α$ -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton is $η$ -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian $α$ -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian...

On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu (2011)

Colloquium Mathematicae

Similarity:

We give sufficient conditions on Banach spaces E and F so that their projective tensor product $E \otimes_{π} F$ and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then $(E \otimes_{ϵ} F) *$ does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is...

The natural operators lifting connections to higher order cotangent bundles

Włodzimierz M. Mikulski (2014)

Czechoslovak Mathematical Journal

Similarity:

We prove that the problem of finding all $ℳ f_{m}$ -natural operators $C : Q ⇝ Q T^{r *}$ lifting classical linear connections $\nabla$ on $m$ -manifolds $M$ into classical linear connections $C_{M} (\nabla)$ on the $r$ -th order cotangent bundle $T^{r *} M = J^{r} {(M, ℝ)}_{0}$ of $M$ can be reduced to the well known one of describing all $ℳ f_{m}$ -natural operators $D : Q ⇝ ⨂^{p} T \otimes ⨂^{q} T^{*}$ sending classical linear connections $\nabla$ on $m$ -manifolds $M$ into tensor fields $D_{M} (\nabla)$ of type $(p, q)$ on $M$ .

On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions

Gopal Ghosh, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $ξ$ belonging to the ${(k, μ)}^{'}$ -nullity distribution and $(k, μ)$ -nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $ξ$ belonging to ${(k, μ)}^{'}$ - and $(k, μ)$ -nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $ξ$ belonging to ${(k, μ)}^{'}$ -nullity...

On infinitesimal transformations preserving the curvature tensor field and its covariant differentials

K. Nomizu, K. Yano (1964)

Annales de l'institut Fourier

Similarity:

On dit qu’une transformation infinitésimale $X$ sur une variété riemannienne $M$ si l’on a $L_{X} (\nabla^{m} R) = 0$ pour tout $m \geq 0$ , où $L_{X}$ est la dérivation de Lie et $\nabla^{m} R$ est le différentiel covariant d’ordre $m$ du champ de tenseurs de courbure $R$ . On démontre que si $M$ est analytique, irréductible et de dimension $\geq 2$ , alors une telle transformation infinitésimale $X$ respecte la connexion riemannienne (et donc la métrique elle-même si $M$ est d’ailleurs complète). On établit aussi une généralisation au cas réductible. ...

On Uniqueness Theoremsfor Ricci Tensor

Marina B. Khripunova, Sergey E. Stepanov, Irina I. Tsyganok, Josef Mikeš (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$ , construct a metric on $M$ whose Ricci tensor equals $r$ . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with...