The curved part of a saddle is called the "seat."
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"
Saddle can be a noun or a verb.
the back of the saddle is the cantle
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
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.
The Cinch. its part of the saddle, and theres also the saying "it'll be a cinch" meaning it will be easy.