Consider first the case of the flat conformal geometry in Euclidean signature.

Conformal geometry - the study of conformal transformations on a space.

Despite these differences, conformal geometry is still tractable.

All such metrics determine the same conformal geometry.

This construction plays a role in algebraic geometry and conformal geometry.

More formally, it is the group of transformations that preserve the conformal geometry of the space.

Then S is the projective (or Möbius) model of conformal geometry.

In two real dimensions, conformal geometry is precisely the geometry of Riemann surfaces.

Thus two dimensional conformal geometry is identical with the study of two-dimensional Möbius geometry.

Conformal geometry has a number of features which distinguish it from (pseudo-)Riemannian geometry.

Circle packings and discrete conformal geometry.

The operator is especially important in conformal geometry, because in a suitable sense it depends only on the conformal structure.

The general theory of conformal geometry is similar, although with some differences, in the cases of Euclidean and pseudo-Euclidean signature.

In this way, the flat model of conformal geometry is the sphere with and P the stabilizer of a point in .

In conformal geometry there is a Weitzenböck formula relating a particular pair of differential operators defined on the tractor bundle.

He made decisive contributions to meromorphic curves, value distribution theory, Riemann surfaces, conformal geometry, quasiconformal mappings and other areas during his career.

This decomposition is known as the Ricci decomposition, and plays an important role in the conformal geometry of Riemannian manifolds.

The round metric is therefore not intrinsic to the Riemann sphere, since "roundness" is not an invariant of conformal geometry.

The Weyl tensor in Riemannian geometry is of major importance in understanding the nature of conformal geometry.

The inversive model of conformal geometry consists of the group of local transformations on the Euclidean space E generated by inversion in spheres.

The Shape Dynamics Formulation of gravity possesses a physical Hamiltonian that generates evolution of spatial conformal geometry.

The replacement of the spacetime picture with a picture of evolving spatial conformal geometry opens the door for a number of new approaches to quantum gravity.

In conformal geometry, the conformal Killing equation on a manifold of space-dimension n with metric describes those vector fields which preserve up to scale, i.e.

Rosenhahn, B. "Pose Estimation of 3D Free-form Contours in Conformal Geometry."

Monge-Ampère equations arise naturally in several problems in Riemannian geometry, conformal geometry, and CR geometry.