#### 100 Citations

A Curvature Identity on a 4-Dimensional Riemannian Manifold

- Mathematics
- 2010

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

On Cosymplectic Conformal Connections

- Mathematics
- 2021

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

Singularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose

- Philosophy, Physics
- 2021

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

Gauging the Spacetime Metric—Looking Back and Forth a Century Later

- Mathematics, Physics
- 2019

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

Gravitational waves in conformal gravity

- Physics
- 2017

Abstract We consider the gravitational radiation in conformal gravity theory. We perturb the metric from flat Mikowski space and obtain the wave equation after introducing the appropriate… Expand

Gravitation and cosmology with York time

- Physics
- 2016

[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

Quantum mechanics as the dynamical geometry of trajectories

- Physics
- 2015

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

2+1 gravity on the conformal sphere

- Physics
- 2013

We show that there are two equivalent first order descriptions of $2+1$ gravity with a nonzero cosmological constant. One is the well-known spacetime description, and the other is in terms of… Expand

Test of conformal gravity with astrophysical observations

- Physics
- 2013

Since it can describe the rotation curves of galaxies without dark matter and can give rise to accelerated expansion, conformal gravity attracts much attention recently. As a theory of modified… Expand

SPACE–TIME STRUCTURE AND SPINOR GEOMETRY

- Physics
- The ANZIAM Journal
- 2008

Abstract The structure of space–time is examined by extending the standard Lorentz connection group to its complex covering group, operating on a 16-dimensional “spinor” frame. A Hamiltonian… Expand