What does traditional German grammar say about a phrase that (at least superficially) centers on a noun, for example, as in this (from Kafka's Der Verschollene)?
»Wer ist auf dem Gang?« ertönte Klaras Stimme, und man sah sie aus einer nahen Tür sich vorbeugen, eine große Tischlampe mit rotem Schirm in der Hand.
By “centering” I mean:
Everything else in the phrase hangs on the noun. In the sample, eine determines Tischlampe, and große and mit rotem Schirm in der Hand modify it.
The noun itself is not connected to the rest of the sentence by any visible connector.
In response to the helpful comments requesting that I be more specific about what I actually want to know, I will say that I would like references to published text on grammatical treatment of noun centered phrases as defined above (though I will also accept the substance of such treatment as remembered by the member providing the answer). I think a phrase “organized around a noun and lacking an obvious connection to the rest of the sentence” is a conspicuous phenomenon, and it is not unreasonable to expect that grammatical attention would have been paid to it.
For example, a grammatical treatment might (a) assimilate the phrase to a broader class of noun-centered phrases (other examples being time expressions like eines Tages), (b) give that class a convenient name, (c) state that the noun must be in the accusative in the subclass to which the Tischlampe example belongs (perhaps tracing the requirement to a Greek or Latin origin), and (d) analyze the phrases as adverbial and modifying the whole sentence in which they occur.
You don’t need to read what is below to answer the question.
To this earlier post, I got the answer that den Rücken der Türe zugewendet was a shortened form of der der Türe den Rücken zugewendet hat. (So the phrase ends up modifying a noun antecedent, ein Herr.) As interesting as it was, the analysis wasn’t entirely satisfying because it depended on the fortuitous presence of a participle and could not be generalized to cover a broader class of phrases.
To this post in English StackExchange, I got the answer that her chin on the table top was short for with her chin on the table top. This was unsatisfying because the analysis was English specific. (You couldn’t similarly say that the German equivalent had a suppressed mit as it would require a dative.) I expect that traditional grammar would have invented a scheme that covers these closely related languages. For instance, French also gives you examples like this (from Camus's L’Étranger):
La garde était aussi au fond, le dos tourné.