Is expiation (kaffarah) obligatory for someone who swore not to enter pornographic websites, then entered one of them, took a fleeting glance, and closed it?

If your soul tempts you to look at what is forbidden, then remember Allah's gaze upon you and His knowledge of your state, and the Day of Judgment and what will transpire therein. Repentance has conditions, in addition to an expiation for an oath for opening the aforementioned website.