Love rivals

Villains or heroes that act as a hero (villain)'s rival over a love interest. Sometimes they want a hero's love interest to like them but when the feelings are not returned, they'll try to kill the hero and then force the love interest to marry them or the hero loves someone who is on villain's side.

The best example would be Gaston. After failing to propose to Belle and learning she was in love with the Beast, he decided to try and kill him so Belle would be his.

A fan fic example of two heroes being rivals over a love interest is Hilda. Initially thinking she is Lincoln's lover and Lydia is Lincoln's best friend and that she is in a friend vs lover scenario. Hilda eventually realizes that Lydia is in love with Lincoln like Hilda, As a result Hilda shows possessive and jealous tendencies towards the red headed heroine for trying to steal Lincoln from her. Played with in that Hilda is aware of Lincoln having many girls into him, but only takes issues with Lydia's closeness with Lincoln among the many girls who like him.