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Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

The tangent space at a point p in an abstract manifold M can be described without the use of embeddings or coordinate charts. The elements of the tangent space are called ...

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

A knot K embedded in R^3=C_z×R_t, where the three-dimensional space R^3 is represented as a direct product of a complex line C with coordinate z and a real line R with ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

One of the eight regions of space defined by the eight possible combinations of signs (+/-,+/-,+/-) for x, y, and z.

The point at which a curve or function crosses the x-axis (i.e., when y=0 in two dimensions).

The point at which a curve or function crosses the y-axis (i.e., when x=0 in two dimensions).

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

Dürer's solid, also known as the truncated triangular trapezohedron, is the 8-faced solid depicted in an engraving entitled Melencolia I by Albrecht Dürer (The British ...