Distinguished connections on $(J^{2}=\pm 1)$-metric manifolds

Fernando Etayo; Rafael Santamaría

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Displaying similar documents to “Distinguished connections on $(J^{2} = \pm 1)$ -metric manifolds”

The natural operators lifting connections to higher order cotangent bundles

Włodzimierz M. Mikulski (2014)

Czechoslovak Mathematical Journal

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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 "special" fibred coordinates for general and classical connections

Włodzimierz M. Mikulski (2010)

Annales Polonici Mathematici

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Using a general connection Γ on a fibred manifold p:Y → M and a torsion free classical linear connection ∇ on M, we distinguish some “special” fibred coordinate systems on Y, and then we construct a general connection $\tilde{ℱ} (Γ, \nabla)$ on Fp:FY → FM for any vector bundle functor F: ℳ f → of finite order.

Bundle functors with the point property which admit prolongation of connections

W. M. Mikulski (2010)

Annales Polonici Mathematici

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Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an $ℱ ℳ_{m, n}$ -canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.

Bi-Legendrian connections

Beniamino Cappelletti Montano (2005)

Annales Polonici Mathematici

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We define the concept of a bi-Legendrian connection associated to a bi-Legendrian structure on an almost -manifold $M^{2 n + r}$ . Among other things, we compute the torsion of this connection and prove that the curvature vanishes along the leaves of the bi-Legendrian structure. Moreover, we prove that if the bi-Legendrian connection is flat, then the bi-Legendrian structure is locally equivalent to the standard structure on $ℝ^{2 n + r}$ .

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.

A construction of a connection on $G Y \to Y$ from a connection on $Y \to M$ by means of classical linear connections on $M$ and $Y$

Włodzimierz M. Mikulski (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let $G$ be a bundle functor of order $(r, s, q)$ , $s \geq r \leq q$ , on the category $ℱ ℳ_{m, n}$ of $(m, n)$ -dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $Γ$ on an $ℱ ℳ_{m, n}$ -object $Y \to M$ we construct a general connection $𝒢 (Γ, λ, Λ)$ on $G Y \to Y$ be means of an auxiliary $q$ -th order linear connection $λ$ on $M$ and an $s$ -th order linear connection $Λ$ on $Y$ . Then we construct a general connection $𝒢 (Γ, \nabla_{1}, \nabla_{2})$ on $G Y \to Y$ by means of auxiliary classical linear connections $\nabla_{1}$ on $M$ and $\nabla_{2}$ on $Y$ . In the case $G = J^{1}$ we determine all general connections...

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir Baghban, Esmaeil Abedi (2018)

Communications in Mathematics

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In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced $(0, 2)$ -tensor on the tangent bundle using these structures and Liouville $1$ -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

Displaying similar documents to “Distinguished connections on ( J 2 = ± 1 ) -metric manifolds”

The natural operators lifting connections to higher order cotangent bundles

On "special" fibred coordinates for general and classical connections

Bundle functors with the point property which admit prolongation of connections

Bi-Legendrian connections

How many are equiaffine connections with torsion

A construction of a connection on G Y → Y from a connection on Y → M by means of classical linear connections on M and Y

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Displaying similar documents to “Distinguished connections on $(J^{2} = \pm 1)$ -metric manifolds”

A construction of a connection on $G Y \to Y$ from a connection on $Y \to M$ by means of classical linear connections on $M$ and $Y$