Classification of k-forms on Rn and the existence of associated geometry on manifolds

0523871 - MÚ 2021 RIV RU eng J - Journal Article
Le, Hong-Van - Vanžura, Jiří
Classification of k-forms on Rn and the existence of associated geometry on manifolds.
Chebyshevskii Sbornik. Roč. 21, č. 2 (2020), s. 362-382. ISSN 2226-8383
R&D Projects: GA ČR(CZ) GA18-00496S
Institutional support: RVO:67985840
Keywords : geometry defined by differential forms * Galois cohomology
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.22405/2226-8383-2020-21-2-362-382

In this paper we survey methods and results of classification of 𝑘-forms (resp. 𝑘-vectors on R𝑛), understood as description of the orbit space of the standard GL(𝑛,R)-action on Λ𝑘R𝑛* (resp. on Λ𝑘R𝑛). 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.
Permanent Link: http://hdl.handle.net/11104/0308148