3 citations · 5 across the 4 of their papers we have counts for
4 papers
Locally Metric Spacetimes
Richard Atkins
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connecti…
When is a Connection a Levi-Civita Connection?
Richard Atkins
We consider the more general question as to when a connection is a metric connection. There are two aspects to this investigation: first, the determination of the integrability con…
On Parallel Sections of a Vector Bundle
Richard Atkins
We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the…
Cohomology and MP Spacetimes
Richard Atkins
This paper pursues a cohomological formulation for gravitation in which gravity might be expressed in terms of a gravitational potential, much in the spirit of electrodynamics. To…