3 citations · 9 across the 11 of their papers we have counts for
11 papers
Ricci Curvature and Gauss Maps of Minimal Submanifolds
Richard Atkins
We present conditions on the Ricci curvature for complete, oriented, minimal submanifolds of Euclidean space, as well as the standard unit sphere, when the Gauss maps are bounded e…
The Lie Algebra of Local Killing Fields
Richard Atkins
We present an algebraic procedure that finds the Lie algebra of the local Killing fields of a smooth metric. In particular, we determine the number of independent local Killing fie…
The Newtonian Potential in Gravitational Cohomology
Richard Atkins
We examine the Newtonian potential in gravitational cohomology. This is given by a symmetric, two-index tensor field, which satisfies the wave equation in empty space. Furthermore,…
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…