- In
projective geometry, a
collineation is a one-to-one and onto map (a bijection) from one
projective space to another, or from a
projective space to itself...
- is a
bijection that maps
lines to lines, and thus a
collineation. In general, some
collineations are not homographies, but the
fundamental theorem of...
- A
curvature collineation (often
abbreviated to CC) is
vector field which preserves the
Riemann tensor in the
sense that, L X R a b c d = 0 {\displaystyle...
- the plane, the
collineation group is
doubly transitive meaning that any
ordered pair of
points can be
mapped by at
least one
collineation to any
other ordered...
- A
matter collineation (sometimes
matter symmetry and
abbreviated to MC) is a
vector field that
satisfies the condition, L X T a b = 0 {\displaystyle {\mathcal...
- the
collineations of PG(2, K) are
compositions of
homographies and
automorphic collineations.
Automorphic collineations are
planar collineations. A projective...
- is
called a
perspective collineation (central
collineation in more
modern terminology). Let φ be a
perspective collineation of S2. Each
point of the...
-
projective space. A
related group is the
collineation group,
which is
defined axiomatically. A
collineation is an
invertible (or more
generally one-to-one)...
-
least three elements, the
first condition can be
simplified to: f is a
collineation, that is, it maps
lines to lines. By the
definition of an
affine space...
- An
affine vector field (sometimes
affine collineation or affine) is a
projective vector field preserving geodesics and
preserving the
affine parameter...
