The author uses the concept of the first principal prolongation of an arbitrary principal filter bundle to develop an alternative procedure for constructing the prolongations of a class of the first-order -structures. The motivation comes from the almost Hermitian structures, which can be defined either as standard first-order structures, or higher-order structures, but if they do not admit a torsion-free connection, the classical constructions fail in general.
@article{701569,
title = {The principal prolongation of first order $G$-structures},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1996},
pages = {[123]-131},
mrnumber = {MR1396607},
zbl = {0863.53020},
url = {http://dml.mathdoc.fr/item/701569}
}
Slovák, Jan. The principal prolongation of first order $G$-structures, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1996), pp. [123]-131. http://gdmltest.u-ga.fr/item/701569/