The curved part of a saddle is called the "seat."
I
meniscus
A roping saddle , which is a Western type of saddle , has a 'slick fork' which facilitates the dismount of the rider ~ see related link below .
Its called the "waist"
the back of the saddle is the cantle
Saddle can be a noun or a verb.
frame The hard part of a saddle is called a saddle tree.
A saddle bow is the front part of a saddle, arched up like a bow.
by cutting the curved part.
curved keel
The seat in which you sit on when on a horses back is called a saddle. The front part of a saddle is called a pommel and the back part of a saddle is called a cantle. Here is a basic saddle the stirrups are not on it at the moment. They are above the saddle not yet attatched.
It does not have a name, it does not exist.
The main difference is that a Western saddle has a horn, while an English saddle does not.