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 ≥ 1 and n ≥ 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 → ℝ and J ₀ r - 1 T ℝ m → 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...