conformal geometry

Noun

conformal geometry (countable and uncountable, plural conformal geometries)

1. The study of conformal (angle-preserving) transformations on a space;
   • Generally, conformal geometries naturally appear at infinity for negatively curved Riemannian geometries. Moreover, due to M. Gromov's [5, 6] geometric approach to infinite groups, conformal geometry invents new fruitful methods in combinatorial group theory.2000, Boris N. Apanasov, Conformal Geometry of Discrete Groups and Manifolds, Walther de Gruyter, page vii
   • The lectures concerned the study of some non-linear partial differential equations related to curvature invariants in conformal geometry.2004, Sun-Yung Alice Chang, Non-linear Elliptic Equations in Conformal Geometry, European Mathematical Society, page 2
2. (formal) an ordered pair comprising a space and the group of conformal transformations that act on the space.