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

Fernando Etayo; Rafael Santamaría

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 classification of the torsion tensors on almost contact manifolds with B-metric

Mancho Manev, Miroslava Ivanova (2014)

Open Mathematics

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The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

Geometry of manifolds which admit conservation laws

David E. Blair, Alexander P. Stone (1971)

Annales de l'institut Fourier

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Let $M$ be an $(n + 1)$ -dimensional Riemannian manifold admitting a covariant constant endomorphism $h$ of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that $M$ is locally flat, a manifold $N$ immersed in $M$ is studied. The manifold $N$ has an induced structure with $n$ of the same eigenvalues if and only if the normal to $N$ is a fixed direction of $h$ . Finally conditions under which $N$ is invariant under $h$ , $N$ is totally geodesic and the induced structure has vanishing...

On prolongations of projectable connections

Jan Kurek, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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We extend the concept of r-order connections on fibred manifolds to the one of (r,s,q)-order projectable connections on fibred-fibred manifolds, where r,s,q are arbitrary non-negative integers with s ≥ r ≤ q. Similarly to the fibred manifold case, given a bundle functor F of order r on (m₁,m₂,n₁,n₂)-dimensional fibred-fibred manifolds Y → M, we construct a general connection ℱ(Γ,Λ):FY → J¹FY on FY → M from a projectable general (i.e. (1,1,1)-order) connection $Γ : Y \to J^{1, 1, 1} Y$ on Y → M by means of an...

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

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