You may need a visa for Cayman Islands if you have a South Korean passport
Visa options for Cayman Islands
Visitor visa
Travellers need a visa to visit Cayman Islands for Business or Tourism. A paper or embassy visa is the only visa available for travellers visiting Cayman Islands. The visa is typically a stamp or sticker added to the passport. Travellers must obtain this visa from a local embassy, consulate or visa center before travelling.