Aeka is the first princess of Jurai. After Yosho left to battle Ryoko and never returned she was in line to the throne. She competes with Ryoko for Tenchi's affection(apparently Juraians feel inbreeding is ok); which is why I think Ryoko should get Tenchi. She unlike Ryoko is prim and proper(she's also into something else as we learn from a song that she sings...), who is more of a free spirit.

Aeka has two guardians(Azaka and Kamidaka), who can appears at any time to protect her when needed. Other than these two she can call upon smaller guardians which can shield her to fire energy blasts. They can also be used as a containment field to protect her or to restrain someone(like Ryoko).

Aeka ship Ryu-oh was damaged to the point where it could not fly after Ryoko crashed it and Ryo-Ohki into the lake in OVA ep.02. Later it was used in the battle against Kagato, where it was destroyed after a failed attempt to break through the Soja's defense line. The only remained og Ryu-oh after the battle was the seed, which was planted in a shell that was designed by Kagato to hold Tsunami. While in the TV series Aeka used Ryu-Oh to try to kill both her and Ryoko in a fit of temporary insanity. After, both ships crashed into the earth all that was left of Ryu-Oh was a seed which she planted in the middle of the lake where it grew quite nicely.

Even though she deeply loves Tenchi, her father, Azusa(King of Jurai) does not approve of the relationship. He had arranged for her to be married with Serio(*cough* fruit). In the last episode of the OVA Tenchi had to fight Serio so Aeka and Sasami can stay on Earth, so that Ryoko does not have to pay her debt, and so the engagement could be broken off. Tenchi "defeated" Serio in that "battle" and the engagement was called off.