Is it obligatory to fulfill a vow to give a third of one's salary to the poor, a third to one's mother, and the rest for oneself, regardless of whether one said, "A promise upon me before God," or not?

For a vow (nadhr) to be valid, it must include a formula that expresses commitment as an act of drawing closer to God Almighty.

The phrase: "When I travel, I will give [charity/money]" does not inherently indicate commitment and thus does not constitute a vow, unless the speaker uttered it with the intention of making a vow, in which case it becomes a vow by virtue of their intention.

As for the phrase: "A promise upon me before God," the questioner is not certain about it, and the default is its absence. Therefore, a ruling should not be made based on it merely due to doubt and possibility.