On the Courant bracket on couples of vector fields and -forms
Miroslav Doupovec; Jan Kurek; Włodzimierz Mikulski
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2018)
- Volume: 72, Issue: 2
- ISSN: 0365-1029
Access Full Article
top
Abstract
topHow to cite
topMiroslav 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- Coimbra, A., Minasian, R., Triendl, H.,Waldram, D., Generalized geometry for string corrections, J. High Energy Phys. 2014 (11) (2014), 160.
- Courant, T. J., Dirac manifolds, Trans. Amer. Math. Soc. 319 (2) (1990), 631-661.
- 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.
- 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.
- 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.
- Gualtieri, M., Generalized complex geometry, Ann. of Math. (2) 174 (1) (2011), 75-123.
- Hitchin, N., Generalized Calabi-Yau manifolds, Q. J. Math. 54 (3) (2003), 281-308.
- Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
- Kurek, J., Mikulski, W. M., The natural linear operators , Colloq. Math. 95 (1) (2003), 37-47.
- Mikulski, W. M., Liftings of 1-forms to the linear r-tangent bundle, Arch. Math. (Brno) 31 (2) (1995), 97-111.
NotesEmbed ?
topYou 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.