What is the ruling on marrying after the death of one's wife, knowing that he had promised her, in jest, before her death that he would not marry?

Fulfilling a promise to remain unmarried after the death of one's wife is not obligatory, and there is no sin in marrying afterward. In fact, it might become obligatory if one fears falling into sin. It is important to note that joking should be truthful, and it is not permissible to lie in it.