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

Miroslav Doupovec; Jan Kurek; Włodzimierz Mikulski

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2018)

  • Volume: 72, Issue: 2
  • ISSN: 0365-1029

Abstract

top
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.

How to cite

top

Miroslav Doupovec, Jan Kurek, and Włodzimierz Mikulski. "On the Courant bracket on couples of vector fields and $p$-forms." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 72.2 (2018): null. <http://eudml.org/doc/290761>.

@article{MiroslavDoupovec2018,
abstract = {If $m\ge p+1\ge 2$ (or $m=p\ge 3$), 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.},
author = {Miroslav Doupovec, Jan Kurek, Włodzimierz Mikulski},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Natural operator; vector field; p-form},
language = {eng},
number = {2},
pages = {null},
title = {On the Courant bracket on couples of vector fields and $p$-forms},
url = {http://eudml.org/doc/290761},
volume = {72},
year = {2018},
}

TY - JOUR
AU - Miroslav Doupovec
AU - Jan Kurek
AU - Włodzimierz Mikulski
TI - On the Courant bracket on couples of vector fields and $p$-forms
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2018
VL - 72
IS - 2
SP - null
AB - If $m\ge p+1\ge 2$ (or $m=p\ge 3$), 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.
LA - eng
KW - Natural operator; vector field; p-form
UR - http://eudml.org/doc/290761
ER -

References

top
  1. Coimbra, A., Minasian, R., Triendl, H.,Waldram, D., Generalized geometry for string corrections, J. High Energy Phys. 2014 (11) (2014), 160. 
  2. Courant, T. J., Dirac manifolds, Trans. Amer. Math. Soc. 319 (2) (1990), 631-661. 
  3. Doupovec, M., Kurek, J., Lifts of tensor fields to the cotangent bundle, in: Differential Geometry and Applications (Brno, 1995), Masaryk University, Brno, 1996, 141-150. 
  4. Doupovec, M., Kurek, J., Mikulski, W. M., The natural brackets on couples of vector fields and 1-forms, Turkish J. Math. 42 (4) (2018), 1853-1862. 
  5. Dębecki, J., Linear liftings of skew symmetric tensor fields of type (1,2) to Weil bundles, Czechoslovak Math. J. 60(135) (4) (2010), 933-943. 
  6. Gualtieri, M., Generalized complex geometry, Ann. of Math. (2) 174 (1) (2011), 75-123. 
  7. Hitchin, N., Generalized Calabi-Yau manifolds, Q. J. Math. 54 (3) (2003), 281-308. 
  8. Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. 
  9. Kurek, J., Mikulski, W. M., The natural linear operators T * T T ( r ) , Colloq. Math. 95 (1) (2003), 37-47. 
  10. Mikulski, W. M., Liftings of 1-forms to the linear r-tangent bundle, Arch. Math. (Brno) 31 (2) (1995), 97-111. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.