Geometry of Anamorphic Projections

Geometry of Oblique Projections

Let A be a unital C-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections P a determined by the diierent involutions # a induced by positive invertible elements a 2 A. The maps ' p : P ! P a sending p to the unique q 2 P a with the same range as p and a : P a ! P sending q to the unitary part of the polar decomposition ...

“ Polytope Projections ” ( Discrete Geometry

Discrete Geometry and Projections

This book is devoted to a discrete Radon transform named the Mojette transform. The Radon transform specificity is to mix Cartesian and radial views of the plane. However, it is straightforward to obtain a discrete lattice from a Cartesian grid while it is impossible from a standard equiangular radial grid. The only mathematical tool is to use discrete geometry that replaces the equiangular rad...

The Anamorphic Universe the Anamorphic Universe

We introduce “anamorphic” cosmology, an approach for explaining the smoothness and flatness of the universe on large scales and the generation of a nearly scale-invariant spectrum of adiabatic density perturbations. The defining feature is a smoothing phase that acts like a contracting universe based on some Weyl frame-invariant criteria and an expanding universe based on other frame-invariant ...

Generic Geometry, Transversality and Projections

In the paper [4] Montaldi proves a powerful transversality result which has a number of applications to the study of the generic geometry of submanifolds of Euclidean or projective space. As a typical application one can consider the contact of surfaces with spheres in Euclidean 3-space and describe the singularities that occur generically and, consequently, the local structure of the focal and...