On the Courant bracket on couples of vector fields and p-forms

Abstract

If m >= p+1 >= 2 (or m = p >= 3), all natural bilinear operators A transforming pairs of couples of vector fields and p-forms on m-manifolds M into couples of vector fields and p-forms on M are described. It is observed that any natural skew-symmetric bilinear operator A as above coincides with the generalized Courant bracket up to three (two, respectively) real constants.

Authors and Affiliations

Miroslav Doupovec, Jan Kurek, Włodzimierz Mikulski

Keywords

Related Articles

Properties of modulus of monotonicity and Opial property in direct sums

We give an example of a Banach lattice with a non-convex modulus of monotonicity, which disproves a claim made in the literature. Results on preservation of the non-strict Opial property and Opial property under passing...

On the Courant bracket on couples of vector fields and p-forms

If m >= p+1 >= 2 (or m = p >= 3), all natural bilinear operators A transforming pairs of couples of vector fields and p-forms on m-manifolds M into couples of vector fields and p-forms on M are described. It is observed...

On almost complex structures from classical linear connections

Let Mfm be the category of m-dimensional manifolds and local diffeomorphisms and let T be the tangent functor on Mfm. Let V be the category of real vector spaces and linear maps and let Vm be the category of m-dimension...

The natural operators of general affine connections into general affine connections

We reduce the problem of describing all Mfm-natural operators transforming general affine connections on m-manifolds into general affine ones to the known description of all GL(Rm)-invariant maps Rm∗⊗Rm→⊗kRm∗⊗⊗kRm for k...

The constructions of general connections on the fibred product of q copies of the first jet prolongation

We describe all natural operators A transforming general connections Gamma on fibred manifolds Y -> M and torsion-free classical linear connections Gamma on M into general connections A(Gamma, Lambda) on the fibred produ...

Download PDF file
  • EP ID EP530759
  • DOI 10.17951/a.2018.72.2.29
  • Views 92
  • Downloads 0

How To Cite

Miroslav Doupovec, Jan Kurek, Włodzimierz Mikulski (2018). On the Courant bracket on couples of vector fields and p-forms. Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica, 72(2), 29-36. https://europub.co.uk/articles/-A-530759