How many are equiaffine connections with torsion

Zdeněk Dušek; Oldřich Kowalski

Displaying similar documents to “How many are equiaffine connections with torsion”

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 $𝒱$ .

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.

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...

On torsion of a $3$ -web

Alena Vanžurová (1995)

Mathematica Bohemica

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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...

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...

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...

On prolongation of connections

Włodzimierz M. Mikulski (2010)

Annales Polonici Mathematici

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Let Y → M be a fibred manifold with m-dimensional base and n-dimensional fibres. Let r, m,n be positive integers. We present a construction $B^{r}$ of rth order holonomic connections $B^{r} (Γ, \nabla) : Y \to J^{r} Y$ on Y → M from general connections Γ:Y → J¹Y on Y → M by means of torsion free classical linear connections ∇ on M. Then we prove that any construction B of rth order holonomic connections $B (Γ, \nabla) : Y \to J^{r} Y$ on Y → M from general connections Γ:Y → J¹Y on Y → M by means of torsion free classical linear connections ∇ on M is equal...

Tensor products of higher almost split sequences in subcategories

Xiaojian Lu, Deren Luo (2023)

Czechoslovak Mathematical Journal

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We introduce the algebras satisfying the $(ℬ, n)$ condition. If $Λ$ , $Γ$ are algebras satisfying the $(ℬ, n)$ , $(ℰ, m)$ condition, respectively, we give a construction of $(m + n)$ -almost split sequences in some subcategories ${(ℬ \otimes ℰ)}^{(i_{0}, j_{0})}$ of $mod (Λ \otimes Γ)$ by tensor products and mapping cones. Moreover, we prove that the tensor product algebra $Λ \otimes Γ$ satisfies the $({(ℬ \otimes ℰ)}^{(i_{0}, j_{0})}, n + m)$ condition for some integers $i_{0}$ , $j_{0}$ ; this construction unifies and extends the work of A. Pasquali (2017), (2019).

Structure of second-order symmetric Lorentzian manifolds

Oihane F. Blanco, Miguel Sánchez, José M. Senovilla (2013)

Journal of the European Mathematical Society

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$𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠$ , that is to say, Lorentzian manifolds with vanishing second derivative $\nabla \nabla R \equiv 0$ of the curvature tensor $R$ , are characterized by several geometric properties, and explicitly presented. Locally, they are a product $M = M_{1} \times M_{2}$ where each factor is uniquely determined as follows: $M_{2}$ is a Riemannian symmetric space and $M_{1}$ is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., $\nabla R \neq 0$ at some point), the curvature...