- In mathematics,
codimension is a
basic geometric idea that
applies to
subspaces in
vector spaces, to
submanifolds in manifolds, and
suitable subsets of...
- In
algebraic geometry,
divisors are a
generalization of
codimension-1
subvarieties of
algebraic varieties. Two
different generalizations are in common...
-
between a
subspace and its
ambient space is
known as its
codimension. A
hyperplane has
codimension 1. In geometry, a
hyperplane of an n-dimensional space...
- bundle, so it
cannot immerse in
codimension 0 (in R 2 {\displaystyle \mathbb {R} ^{2}} ),
though it
embeds in
codimension 1 (in R 3 {\displaystyle \mathbb...
- integrability' of a
hyperplane distribution, i.e. that it be
tangent to a
codimension one
foliation on the manifold,
whose equivalence is the
content of the...
- is
called the
dimension of the
foliation and q = n − p is
called its
codimension. In some
papers on
general relativity by
mathematical physicists, the...
-
stable manifolds of the saddle. In
three or more dimensions,
higher codimension bifurcations can occur,
producing complicated,
possibly chaotic dynamics...
- the
middle dimension has
codimension more than 2: when the
codimension is 2, one
encounters knot theory, but when the
codimension is more than 2, embedding...
-
linear algebra and geometry,
relative dimension is the dual
notion to
codimension. In
linear algebra,
given a
quotient map V → Q {\displaystyle V\to Q}...
-
something happens, it
happens in a
particular codimension". For example,
ramification is a
phenomenon of
codimension 1 (in the
geometry of
complex manifolds...
