Learn German: Bitte hinter der Bahnsteigkante zurückbleiben! - Please stand back behind the platform edge!

Using the infinitive at the very end of a sentence creates an impersonal command. This is a common and formal way to issue instructions or warnings to the general public, which is why you will frequently hear it in train station announcements or read it on signs.

Since the English translation says "stand back" which implies movement, why does hinter take the dative case (der) instead of the accusative (die)?

hinter is a two-way preposition. While the English phrasing implies a motion backward, the German verb zurückbleiben literally means "to stay back" or "to remain behind." Because the verb focuses on maintaining a fixed location rather than moving to a new destination, the preposition takes the dative case.

Because zurückbleiben is a separable verb, why aren't the parts separated here?

They stay together because this impersonal command uses the raw infinitive form of the verb. You only separate the prefix when conjugating the verb in a main clause, such as in the direct command Bleiben Sie bitte zurück!.

How does the compound noun Bahnsteigkante break down?

It is made of three parts: die Bahn (train/railway), der Steig (path/walkway—giving us der Bahnsteig for train platform), and die Kante (edge). As always with German compound nouns, the last word dictates the gender, making it die Bahnsteigkante.