Grassmannians of higher order appeared for the first time in a paper of A. Szybiak in the context of the Cartan method of moving frame. In the present paper we consider a special case of higher order Grassmannian, the projective space of second order. We introduce the projective group of second order acting on this space, derive its Maurer-Cartan equations and show that our generalized projective space is a homogeneous space of this group.
@article{urn:eudml:doc:40629,
title = {Projective spaces of second order.},
journal = {Collectanea Mathematica},
volume = {48},
year = {1997},
pages = {355-362},
zbl = {0905.53037},
mrnumber = {MR1475811},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40629}
}
Miernowski, Andrzej; Mozgawa, Witold. Projective spaces of second order.. Collectanea Mathematica, Tome 48 (1997) pp. 355-362. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40629/