absorbed / recessed
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absorbed
Mentally very focused on something and unaware of one's surroundings.
Sie saß vertieft in ein Buch am Fenster und bemerkte nicht, wie die Zeit verging.
She sat by the window absorbed in a book and didn't notice how time was passing.
'Vertieft' is the past participle of the verb 'vertiefen' (to deepen). It is used as an adjective, and its meanings derive directly from the verb: 'sich in etwas vertiefen' (to become absorbed in something) or 'etwas vertiefen' (to make something deeper).
Er war so in seine Arbeit vertieft, dass er die Zeit vergaß.
He was so absorbed in his work that he forgot the time.
The preposition 'in' helps distinguish the meanings. 'Vertieft in' + accusative describes mental concentration. 'Vertieft in' + dative describes a physical indentation in a material.
Der Forscher war in seine Studien vertieft (Akkusativ).
The researcher was absorbed in his studies (accusative).
When someone is concentrated, they are often 'in ein Buch' (in a book), 'in ein Gespräch' (in a conversation), 'in Gedanken' (in thought), or 'in seine Arbeit' (in their work) 'vertieft' (absorbed).
Die beiden waren in ein langes Gespräch vertieft.
The two of them were absorbed in a long conversation.
attentive / considerate
'aufmerksam' and 'vertieft' both have to do with concentration. You use 'aufmerksam' when someone deliberately listens, watches, or follows something carefully. 'vertieft' means that someone is so deeply occupied with something that they hardly notice their surroundings. Learners may confuse the words because both express concentration. The difference is: 'aufmerksam' fits well with lessons, conversations, or observation. 'vertieft' fits better with reading, working, or thinking, when someone is completely immersed in an activity.
Der Gast war so in sein Buch vertieft, dass er den Kellner nicht bemerkte.
The guest was so absorbed in his book that he did not notice the waiter.
Mein Nachbar ist im Kurs sehr aufmerksam, weil er die Prüfung bestehen möchte.
My neighbor is very attentive in the course because he wants to pass the exam.