Multisymplectic forms of degree three in dimension seven

Bureš, Jarolím, and Vanžura, Jiří. "Multisymplectic forms of degree three in dimension seven." Proceedings of the 22nd Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2003. [73]-91. <http://eudml.org/doc/220797>.

@inProceedings{Bureš2003,
abstract = {A multisymplectic 3-structure on an $n$-dimensional manifold $M$ is given by a closed smooth 3-form $\omega $ of maximal rank on $M$ which is of the same algebraic type at each point of $M$, i.e. they belong to the same orbit under the action of the group $GL(n,\{\mathbb \{R\}\})$. This means that for each point $x\in M$ the form $\omega _x$ is isomorphic to a chosen canonical 3-form on $\{\mathbb \{R\}\}^n$. R. Westwick [Linear Multilinear Algebra 10, 183–204 (1981; Zbl 0464.15001)] and D. Ž. Djoković [Linear Multilinear Algebra 13, 3–39 (1983; Zbl 0515.15011)] obtained the classification of 3-forms in dimension seven. Among these forms they revealed eight being canonical forms. By using these results the authors describe the isotropy groups of all canonical forms. To point out the nature of these eight groups we mention, for example: the exceptional Lie group $G_2$, its noncompact dual $\tilde\{G\}_2$,},
author = {Bureš, Jarolím, Vanžura, Jiří},
booktitle = {Proceedings of the 22nd Winter School "Geometry and Physics"},
keywords = {Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[73]-91},
publisher = {Circolo Matematico di Palermo},
title = {Multisymplectic forms of degree three in dimension seven},
url = {http://eudml.org/doc/220797},
year = {2003},
}

TY - CLSWK
AU - Bureš, Jarolím
AU - Vanžura, Jiří
TI - Multisymplectic forms of degree three in dimension seven
T2 - Proceedings of the 22nd Winter School "Geometry and Physics"
PY - 2003
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [73]
EP - 91
AB - A multisymplectic 3-structure on an $n$-dimensional manifold $M$ is given by a closed smooth 3-form $\omega $ of maximal rank on $M$ which is of the same algebraic type at each point of $M$, i.e. they belong to the same orbit under the action of the group $GL(n,{\mathbb {R}})$. This means that for each point $x\in M$ the form $\omega _x$ is isomorphic to a chosen canonical 3-form on ${\mathbb {R}}^n$. R. Westwick [Linear Multilinear Algebra 10, 183–204 (1981; Zbl 0464.15001)] and D. Ž. Djoković [Linear Multilinear Algebra 13, 3–39 (1983; Zbl 0515.15011)] obtained the classification of 3-forms in dimension seven. Among these forms they revealed eight being canonical forms. By using these results the authors describe the isotropy groups of all canonical forms. To point out the nature of these eight groups we mention, for example: the exceptional Lie group $G_2$, its noncompact dual $\tilde{G}_2$,
KW - Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220797
ER -