Scale-invariant actions in arbitrary dimensions are investigated in curved space to clarify the relation between scale-, Weyland conformal invariance on the classical level. The global Weyl-group is gauged. Then the class of actions is determined for which Weyl-gauging may be replaced by a suitable coupling to the curvature (Ricci gauging). It is shown that this class is exactly the class of ac...

It is shown that the surface gravity and temperature of a stationary black hole are invariant under conformal transformations of the metric that are the identity at infinity. More precisely, we find a conformal invariant definition of the surface gravity of a conformal Killing horizon that agrees with the usual definition(s) for a true Killing horizon and is proportional to the temperature as d...

Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standar...

The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In codimension one we classify such invariants, showing that under a structural ...

3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

A new class of conformal invariants for a given spacetime $M$ is introduced exploiting the geometry any light ray $\Gamma$. Each congruence rays passing through point $p$ defines sky $S(p)$ such point. The are defined on bundle skies $M$, being called accordingly. natural covariant derivative and its associated calculus allows us show existence invariant differential arc that, together with res...