I have Carstens in my tree through my husband's mother's family, the Kaysers.
Christian Wilhelm Carstens, b. 1815, Bokelsess, Schleswig-Holstein, Prussia
Married to Charlotte Elizabeth Koepecke 1818-1869
daughter Sophie Emilie Henriette Carstens 1841 -1887 (all born in the same place) married to Juergen Anton Heinrich Kayser in 1869. Juergen's dates 1843-1928. He was my husband's great-grand uncle.
Niedersachsen was created in 1946 after WW 2. It encompasses the old Kingdom of Hannover and parts of West Prussia.