"He sleeps in the afternoon."
Translation:Han sover om eftermiddagen.
For now, a PDF of Danish: A Practical Grammar by Allan, Holmes and Lundskaer-Nielsen is available on the web.
In the year 2000 edition, "Om" the preposition is discussed at paragraph 121, paper page 125, PDF page 140 of 225.
There are examples of "om" as a preposition of:
- time (in the morning, on Fridays, twice a day, twice per week)
- location surrounding (around the neck)
- subject matter (a book about horses, a dissertation on Locke)
"Om" is also a conjunction ( if - when there is uncertainty or doubt expressed).
Some pages of Danish: A Comprehensive Grammar, the 2015 edition, can be viewed as a google books preview. However, "om" the preposition is discussed mostly on pages that are not available in the preview.
Correct me if I'm wrong, but it seems to me that the difference between "om" and "i" is that "om" is used to indicate time in the general sense, whereas "i" is used to indicate a specific occasion, for example: Han sover om eftermiddagen = every morning. Han sover i eftermiddagen = this particular morning.