A ban on carriage applies for travellers entering Germany from so-called areas of virus variants of concern (overview on the RKI's website; please note that this page contains information in German and English) meaning that those people may not travel to or enter Germany in accordance with the Coronavirus-Einreiseverordnung [Ordinance on Coronavirus Entry Regulations]. The same applies to people who have already been fully vaccinated. Exemptions can be made in very few cases only, e.g. for people with their place of residence and a right of residence in Germany. (information on the Ministry's website; information in English can be obtained by changing the language).
This means that a study or research stay in Germany in the winter semester 2021/22 cannot be ensured for students and researchers from areas classified as areas of virus variants of concern. Please note that entering Germany will also not be possible for those people who were already awarded a place on a degree programme by a German university: As it is not possible to enter Germany visas cannot be issued as long as a country is classified as an area of virus variants of concern.
Please keep yourself updated on the risk assessment for your country.