The principal prolongation of first order \(G\)-structures. (English) Zbl 0863.53020

Slovák, Jan

Bureš, J. (ed.) et al., Proceedings of the Winter School on geometry and physics, Srní, Czech Republic, January 1994. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 39, 123-131 (1996).

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 \(G\)-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.
For the entire collection see [Zbl 0840.00036].

Reviewer: I.Kolář (Brno)

MSC:

53C10	\(G\)-structures
58A20	Jets in global analysis
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53A55	Differential invariants (local theory), geometric objects

Keywords:

first-order \(G\)-structure; almost Hermitian structure; principal prolongation