When people of Amber and the Golden Circle think of Rebma, they think of the ghost city where water can be breathed like air and where Amber City is reflected. They do not think much of what lies past that. Rebma's signature trade is whaling; a pretty extensive range and variety of whales are available to it. It does trade actively with Amber. It's known that Moire has quite a kingdom, but in truth, Rebma is a mystery to nearly all who do not live within its waters.
Rebma is Amber's reflection, and from a metaphysical / shadow travel point of view, all of Amber that lies beneath the sea can be considered to be Rebma. It is essentially as "real" as Amber; one cannot directly shift shadow into Rebma. The outer reaches of Amber's seas are Rebma below the waves, and just as there are shadow-forests that are reflections of Arden, there are shadow-seas that eventually seamlessly become Amber/Rebma.
Rebma's claimed sovereign territory above the waves is known as the Rebman Triangle, and is marked by three lighthouses. (See the Amber map and Rebma wiki for details.) The area claimed by the Triangle is large enough to more than encompass the territory taken up by Rebma City proper.
It is possible to sail between Amber and its shadowpath entrances without entering the Rebman triangle. The shadowpath entrances themselves are patrolled by Amber's Navy; the Rebman Triangle is patrolled by Rebma's Navy.
Any sail from shadow into the Rebman Triangle, whether via a shadowpath or via shadow-shifting, will cross Amber's waters prior to entering the Triangle. Similarly, any sail from the Triangle out into shadow will cross Amber's waters. Rebma still lies below those waters of Amber, but the sovereignty of the waters above are claimed by Amber.
Secrets of Rebma
The information below is known only to those characters who have levels of Lore in Rebma; it is provided here strictly as a reference for character and story ideas.
Those who live beneath the waves know that Rebma is actually a vast aquatic empire, incorporating numerous races and species. It is dotted with ruins of impossible age — ruins often rich with arcane power. These places are sacred to Rebma, and to their perspective, the ghost city is the most sacred of them all. It is the sacred city where the divinely chosen aristocracy of Rebma lives.
Rebma is ruled by the humanoids which most Amberites think of as Rebmans, with Moire as their current queen. There is a great deal of internal conflict over this arrangement, but these matters are kept as hidden as the rest of the empire.
Rebma's magic is particularly distinct; it is the magic of mirrors. Although the more educated are vaguely aware that Rebma's mirror mages are able to perform tricks with the many mirrors reputed to hang in the underwater city, the more essential truth is not known to others is that Rebma is where history goes to die. Mirrors in Rebma accumulate images of history, though there is neither rhyme nor reason to their distribution. Mostly this is trivial — Rebman mirror-pickers effectively have vast collections of snapshots, the majority of which are meaningless, but every now and again there's a rare find.
This is one of the reasons that Rebma favors stability. In times of chaos, the history flows a lot faster, wreaking havoc with whatever small order has been imposed on existing records.
Moire's player maintains a Rebma wiki.