In this section we outline some basic twistor geometry. Let 
be complexified compactified Minkowski space.
(We can think of it as the Grassmannian manifold 
.)
The basic concept is that of incidence.
is incident with a spacetime point 
iff
is incident with a spacetime point 
iff
is incident with 
iff 
.
In the projective twistor space 
, 
defines a point as an equivalence class of all twistors in 
proportinal to 
.
The set of all spacetime points incident with it forms a totally null complex 2-plane in 
(
-plane).
If we denote the incidence relation with 
, then
for all 
.
Any two vectors in the 
-plane are orthogonal to each other.
Since 
and 
have the same incidence properties for 
, it is natural to study incidence on the projective twistor space 
.
Dual twistors now correspond to planes in 
and are incident on 
-planes in 
. These are also totally null complex 2-planes in 
.
Finally, it can be shown that 
iff there is a spacetime point incident on both of them. Geometric correspondence defined by the incidence relation (Klein correspondence) is summarised in the following table:
