Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.
@article{bwmeta1.element.doi-10_2478_s11533-012-0021-y,
author = {Sasha Anan'in and Carlos Grossi},
title = {Differential geometry of grassmannians and the Pl\"ucker map},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {873-884},
zbl = {1244.53056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0021-y}
}
Sasha Anan’in; Carlos Grossi. Differential geometry of grassmannians and the Plücker map. Open Mathematics, Tome 10 (2012) pp. 873-884. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0021-y/
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