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math.DG2008★ 3 cited
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…
math.DG2008★ 1 cited
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…