We revisit a theorem, somehow neglected at present, due to E. Beltrami, through which the integration of the geodesic equations of a curved manifold is obtained by means of a method which, even if inspired by Hamilton-Jacobi method, is merely geometric. The application of this theorem to the Schwarzschild and Kerr metrics allows us to obtain in a straightforward and general way the solution of ...

Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as three-dimensional coordinates each vertex is mapped to, which often requires lots of memory. This causes inconvenience in data transmission and data storage. To tackle this problem, we p...

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that arises naturally as the classical limit; a theory with nonsymmetric metric and a skew version of metric compatibilty. Meanwhile, in quantum gravity a key ingre...

The micromechanical approach to topology design consists in deening a domain of porous material, including the loads and supports, and nding an optimal distribution of the densities. The usual method is to mesh the structure and assign a diierent density and material orientation to every element. Optimal topologies emerge when using the densities and orientations as design variables in a mathem...

An effective action describing N=1, 2d-induced supergravity in the chi-ral gauge is obtained on the supertorus and on a compact SRS without boundary of arbitrary genus. This action integrates the superconformal Ward identity for the superdiffeomorphism anomaly; it yields the last step in the extension to more complicated topologies of the action initially obtained by A.M. Polyakov on the ordina...

Discrete Laplace–Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of the weak Laplace–Beltrami operator are well-studied, less is known about the strong form. We present a principle for constructing strongly consistent discrete Laplace–Beltrami o...