mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, a Lorentz surface is a two-dimensional

oriented In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is ...

smooth manifold with a

conformal equivalence Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface * Plane (mathematics), generalizations of a geometrical plane Plane or planes may also refer to: Biology * Pl ...

class of

Lorentzian metric In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the r ...

s. It is the analogue of a

Riemann surface In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

in indefinite signature.

Further reading