Princess Ayeka of Jurai was summoned to Earth because of Ryoko's antics, and stayed after she fell hopelessly in love with Tenchi. She was originally attracted to Tenchi because of his resemblence to her former fiancee and half-brother (!), Yosho, but now loves Tenchi for who he is.
Ayeka is often seen with her guardians Azaka and Kamidake, and her sister Sasami. Her mother is Misaki and her father is (obviously) the Emperor of Jurai. Ayeka can use her Juraian powers to make energy shields, summon "mini-guardians" to attack or capture others, fire energy bolts, or create a battlesuit. Her spaceship/tree (all Juraians have a tree specific to him/herself) is Ryo-oh, but it was destroyed in a battle with Ryoko and Ryo-Ohki.
Whereas Ryoko is outgoing and flirtatious with Tenchi, Ayeka is usually very quiet and shy, and actually pretends (very unsuccessfully) she's not interested and only trying to save Tenchi from the "ugly ogre". But despite their differences, Ayeka has worked together with Ryoko several times (once to get rid of the extra competition, a.k.a. Washu and Mihoshi).