conformal geometry

conformal +‎ geometry

conformal geometry (countable and uncountable, plural conformal geometries)

1. (geometry) The study of conformal (angle-preserving) transformations on a space;
   (formally) an ordered pair comprising a space and the group of conformal transformations that act on the space.
   • 2000, Boris N. Apanasov, Conformal Geometry of Discrete Groups and Manifolds, Walther de Gruyter, page vii,

     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.

   • 2004, Sun-Yung Alice Chang, Non-linear Elliptic Equations in Conformal Geometry, European Mathematical Society, page 2:

     The lectures concerned the study of some non-linear partial differential equations related to curvature invariants in conformal geometry.

   • 2018, Miao Jin, Xianfeng Gu, Ying He, Yalin Wang, Conformal Geometry: Computational Algorithms and Engineering Applications, Springer, page 1:

     This chapter gives a brief introduction of the basic theoretic foundations and profound and beautiful structures of conformal geometry.

• conformal manifold
• conformal metric
• conformal transformation

• Klein geometry
• Möbius geometry
• pseudo-Riemannian manifold
• Riemann surface
• Riemannian manifold