Geodesic
Classification of $k$-forms on $\mathbb{R}^n$ and the existence of associated geometry on manifolds
Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 362-382

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we survey methods and results of classification of $k$-forms (resp. $k$-vectors on $\mathbb{R}^n$), understood as description of the orbit space of the standard $\mathrm{GL}(n, \mathbb{R})$-action on $\Lambda^k \mathbb{R}^{n*}$ (resp. on $\Lambda ^k \mathbb{R}^n$). We discuss the existence of related geometry defined by differential forms on smooth manifolds. This paper also contains an Appendix by Mikhail Borovoi on Galois cohomology methods for finding real forms of complex orbits.
Keywords: $ \mathrm {GL} (n, {\mathbb R})$-orbits in $\Lambda^k\mathbb{R}^{n*}$, $\theta$-group, geometry defined by differential forms, Galois cohomology. 
@article{CHEB_2020_21_2_a24,
     author = {H\^ong V\^an L\^e and J. Van\v{z}ura},
     title = {Classification of $k$-forms on $\mathbb{R}^n$ and the existence of associated geometry on manifolds},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {362--382},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a24/}
}
TY  - JOUR
AU  - Hông Vân Lê
AU  - J. Vanžura
TI  - Classification of $k$-forms on $\mathbb{R}^n$ and the existence of associated geometry on manifolds
JO  - Čebyševskij sbornik
PY  - 2020
SP  - 362
EP  - 382
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a24/
LA  - en
ID  - CHEB_2020_21_2_a24
ER  - 
%0 Journal Article
%A Hông Vân Lê
%A J. Vanžura
%T Classification of $k$-forms on $\mathbb{R}^n$ and the existence of associated geometry on manifolds
%J Čebyševskij sbornik
%D 2020
%P 362-382
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a24/
%G en
%F CHEB_2020_21_2_a24
Hông Vân Lê; J. Vanžura. Classification of $k$-forms on $\mathbb{R}^n$ and the existence of associated geometry on manifolds. Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 362-382. http://geodesic.mathdoc.fr/item/CHEB_2020_21_2_a24/