Weyl’s original scale geometry of 1918 (“purely infinitesimal geometry”) was withdrawn by its author from physical theorizing in the early 1920s. It made a surprising comeback, however, in the last… Expand

We recall a curvature identity for 4-dimensional compact Riemannian manifolds as derived from the generalized Gauss–Bonnet formula. We extend this curvature identity to non-compact 4-dimensional… Expand

The aim of this paper is to introduce a cosymplectic analouge of conformal connection in a cosymplectic manifold and proved that if cosymplectic manifold M admits a cosymplectic conformal connection… Expand

In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity… Expand

H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It… Expand

During his life Weyl approached the problem of space (PoS) from various sides. Two aspects stand out as permanent features of his different approaches: the unique determination of an affine… Expand

[Shortened abstract:] In this thesis we investigate a solution to the `problem of time' in canonical quantum gravity by splitting spacetime into surfaces of constant mean curvature parameterised by… Expand

We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free… Expand