# What is the meaning of the following sentence? Setze g zu einem

I am trying to read a German math book and I am not sure about exact meaning of the following sentence:

Setze g zu einem metrischen Zusammenhang D fort.

I translate (guess) it as: extend g smoothly to a metric connection D.

which it is a bit meaningless. As far as I understand in a few hours till I started to read a German math book: "fort" is the second component of compound Words "Setze fort" that its translation is: "to continue" or "to proceed". This confused me since it is irrelevant to sentence a bit.

I am sure about translation of "metrischen Zusammenhang D" that is "metric connection D".

• Is there a figure, which shows what g and D are? Jun 18, 2022 at 22:11
• The verb is fortsetzen in a dictionary. It has a number of possible translations, but "extend" is most likely in mathematics. It is a quirk of German that pieces of the main verb can break off and drift to the end of the sentence, so you have to find all the parts and reassemble them in order to look up the word. It takes a while to get used to this and recognize when it's happening, but it's not actually that difficult to understand. Jun 19, 2022 at 2:56
• @RDBury thanks for remark. Jun 19, 2022 at 4:36
• Can you give a little more context? Usually \$g\$ denotes the metric on a manifold \$M\$ and one can build a metric connection from \$g\$, although the construction isn't really an extension. The connection defined from the metric is usually also required to be torsion free (and then called Levi-Civita connection) otherwise you don't get uniqueness. Jun 19, 2022 at 9:13
• You are going into some heavy machinery differential geometry here. If you need the translation of German to English I would recommend getting a German and an English textbook on the topic (wikipedia might suffice). It seems 'fortsetzen' is a someone odd use of the word here but the definition should be the same regardless of language. Jun 19, 2022 at 15:06