Is Projective Geometry the Ultimate Form of Kleinian Geometry?

[Symbreak]

Does anyone know of further geometries beyond projective geometry? Kleinian geometry seems to imply projective geometry is the most general, as objects are more congruent and there are more groups of transformations to underly the congruence. But it seems ad hoc and arbitary to have a limit on congruence - could we not say the most general geometry is that limited to 1-dimensional objects, where all things are points and in one state of congruence?

 

[robphy]

Riemannian Geometry, Finslerian Geometry, Symplectic Geometry, Algebraic Geometry, ...
... http://mathworld.wolfram.com/Geometry.html