What is the meaning of the term "prolongation" in differential geometry? Differential geometers often talk about "prolonging" a system of differential equations, or jet prolongation of bundle sections, but I don't really understand what mental picture the term "prolongation" is supposed to convey. Is it because when you introduce new variables for higher derivatives in a differential equation the system becomes "longer" when you write it down? Is that all there is to it, or is there some better reason for the terminology?
2026-02-23 04:36:12.1771821372
What does prolongation mean in differential geometry?
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