On torsion of a $3$-web

Alena Vanžurová

Displaying similar documents to “On torsion of a $3$ -web”

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

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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 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

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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...

Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

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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...

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

Oğuz Varol (2007)

Studia Mathematica

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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.

Horizontal lift of symmetric connections to the bundle of volume forms $𝒱$

Anna Gasior (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms $𝒱$ and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a $F (3, 1)$ -structure on $𝒱$ .

Canonical Poisson-Nijenhuis structures on higher order tangent bundles

P. M. Kouotchop Wamba (2014)

Annales Polonici Mathematici

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Let M be a smooth manifold of dimension m>0, and denote by $S_{c a n}$ the canonical Nijenhuis tensor on TM. Let Π be a Poisson bivector on M and $Π^{T}$ the complete lift of Π on TM. In a previous paper, we have shown that $(T M, Π^{T}, S_{c a n})$ is a Poisson-Nijenhuis manifold. Recently, the higher order tangent lifts of Poisson manifolds from M to $T^{r} M$ have been studied and some properties were given. Furthermore, the canonical Nijenhuis tensors on $T^{A} M$ are described by A. Cabras and I. Kolář [Arch. Math. (Brno) 38 (2002),...

On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu (2011)

Colloquium Mathematicae

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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...

A Study on $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds

Gurupadavva Ingalahalli, C.S. Bagewadi (2018)

Communications in Mathematics

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In this paper we study $φ$ -recurrence $τ$ -curvature tensor in $(k, μ)$ -contact metric manifolds.

Linear natural operators lifting $p$ -vectors to tensors of type $(q, 0)$ on Weil bundles

Jacek Dębecki (2016)

Czechoslovak Mathematical Journal

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We give a classification of all linear natural operators transforming $p$ -vectors (i.e., skew-symmetric tensor fields of type $(p, 0)$ ) on $n$ -dimensional manifolds $M$ to tensor fields of type $(q, 0)$ on $T^{A} M$ , where $T^{A}$ is a Weil bundle, under the condition that $p \geq 1$ , $n \geq p$ and $n \geq q$ . The main result of the paper states that, roughly speaking, each linear natural operator lifting $p$ -vectors to tensor fields of type $(q, 0)$ on $T^{A}$ is a sum of operators obtained by permuting the indices of the tensor products of linear natural...

Displaying similar documents to “On torsion of a 3 -web”

Displaying similar documents to “On torsion of a $3$ -web”