Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

Josef Janyška

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Displaying similar documents to “Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold”

The natural operators lifting vector fields to generalized higher order tangent bundles

Włodzimierz M. Mikulski (2000)

Archivum Mathematicum

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For natural numbers $r$ and $n$ and a real number $a$ we construct a natural vector bundle $T^{(r), a}$ over $n$ -manifolds such that $T^{(r), 0}$ is the (classical) vector tangent bundle $T^{(r)}$ of order $r$ . For integers $r \geq 1$ and $n \geq 3$ and a real number $a < 0$ we classify all natural operators $T_{| M_{n}} ⇝ T T^{(r), a}$ lifting vector fields from $n$ -manifolds to $T^{(r), a}$ .

Lifting vector fields to the rth order frame bundle

J. Kurek, W. M. Mikulski (2008)

Colloquium Mathematicae

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We describe all natural operators lifting nowhere vanishing vector fields X on m-dimensional manifolds M to vector fields (X) on the rth order frame bundle $L^{r} M = i n v J ₀^{r} (ℝ^{m}, M)$ over M. Next, we describe all natural operators lifting vector fields X on m-manifolds M to vector fields on $L^{r} M$ . In both cases we deduce that the spaces of all operators in question form free $(m (C_{r}^{m + r} - 1) + 1)$ -dimensional modules over algebras of all smooth maps $J ₀^{r - 1} T ̃ ℝ^{m} \to ℝ$ and $J ₀^{r - 1} T ℝ^{m} \to ℝ$ respectively, where $C ⁿ_{k} = n! / (n - k)! k!$ . We explicitly construct bases of these modules. In particular,...

Subfields of henselian valued fields

Ramneek Khassa, Sudesh K. Khanduja (2010)

Colloquium Mathematicae

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Let (K,v) be a henselian valued field of arbitrary rank which is not separably closed. Let k be a subfield of K of finite codimension and $v_{k}$ be the valuation obtained by restricting v to k. We give some necessary and sufficient conditions for $(k, v_{k})$ to be henselian. In particular, it is shown that if k is dense in its henselization, then $(k, v_{k})$ is henselian. We deduce some well known results proved in this direction through other considerations.

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...

On $p^{2}$ -Ranks in the Class Field Tower Problem

Christian Maire, Cam McLeman (2014)

Annales mathématiques Blaise Pascal

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Much recent progress in the 2-class field tower problem revolves around demonstrating infinite such towers for fields – in particular, quadratic fields – whose class groups have large 4-ranks. Generalizing to all primes, we use Golod-Safarevic-type inequalities to analyse the source of the $p^{2}$ -rank of the class group as a quantity of relevance in the $p$ -class field tower problem. We also make significant partial progress toward demonstrating that all real quadratic number fields whose class...

Displaying similar documents to “Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold”

The natural operators lifting vector fields to generalized higher order tangent bundles

Lifting vector fields to the rth order frame bundle

Subfields of henselian valued fields

On torsion of a 3 -web

On p 2 -Ranks in the Class Field Tower Problem

On torsion of a $3$ -web

On $p^{2}$ -Ranks in the Class Field Tower Problem