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In conformal geometry, a conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric (also called a conformal Killing vector, CKV, or conformal colineation), is a vector field whose (locally defined) flow defines conformal transformations, that is, preserve up to scale and preserve the conformal structure.
A conformal manifold is a Riemannian manifold ... Thus the length of a tangent vector cannot be defined, but the angle between two vectors still can.
A conformal linear transformation, also called a homogeneous similarity transformation or homogeneous similitude, is a similarity transformation of a Euclidean or pseudo-Euclidean vector space which fixes the origin.
Given a vertex algebra homomorphism from a Virasoro vertex algebra of central charge c to any other vertex algebra, the vertex operator attached to the image of ω automatically satisfies the Virasoro relations, i.e., the image of ω is a conformal vector. Conversely, any conformal vector in a vertex algebra induces a distinguished vertex ...
If the metric in a conformal class is replaced by the conformally rescaled metric of the same class ^ =, then the Levi-Civita connection transforms according to the rule [12] ^ = + + (,) (). where () is the gradient vector field of i.e. the vector field -dual to , in local coordinates given by ().
Conformal symmetry encompasses special conformal transformations and dilations. ... is a covariant vector under the Lorentz transformations.
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, ... For vector fields, ...
Several specific conformal groups are particularly important: The conformal orthogonal group. If V is a vector space with a quadratic form Q, then the conformal orthogonal group CO(V, Q) is the group of linear transformations T of V for which there exists a scalar λ such that for all x in V = ()