Who killed Ariana Dumbledore ?

Albus Dumbledore
Aberforth Dumbledore
Gellert Grindelwald

Aberforth and Albus fought over the strife in their family. Eventually they came to duel which also involved Gellert Grindelwald. It was during this duel that Ariana was killed. It is unclear who or what caused her accidental death, although Aberforth blamed Albus, and never forgave him.

Aberforth Dumbledore became aware of the pair's research, and opposed them. He attempted to persuade them against their plans, setting Grindelwald on the defensive and resulting in a three-way duel in which Ariana Dumbledore, his sister who had difficulty controlling her magic, was killed. The two Dumbledores were devastated. Albus ended his friendship with Grindelwald and Grindelwald fled, not wanting to be associated with the death

Dumbledore and his brother Aberforth argueed over Albus' neglect of Ariana. When the argument became more heated, Grindelwald attacked Aberforth with the Cruciatus Curse, and a duel ensued. Albus rushed to protect Aberforth, and curses were cast in every direction amongst the confusion. A Killing Curse hit Ariana; though the caster was unknown and the targeting was purely accidental, this haunted Dumbledore for the rest of his life.