Princess Ayeka is the heir to the throne of the planet Jurai. Her sister, Sasami, seems to be her advisor, her being the wiser of the two, even though Ayeka is older. She is searching for her half-brother, Yosho, so that she can fulfill her parents' wish to marry him. (It's not a strange thing to do that on that planet, apparently.) When she and Tenchi first meet, they seem to not like each other one bit. But sooner than she can make the log guardians Azaka and Kamidake attack you, it looks to me like they've fallen in love, which is not in the best interest of Ryoko.