16 citations · 16 across the 4 of their papers we have counts for
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math.DG2012
The Geodesics of Rolling Ball Systems
Daniel R. Cole
A well-known and interesting family of sub-Riemannian space are the systems involving two balls rolling against each other without slipping or twisting. In this note, we show how t…
math.DG2008
A Natural Connection on (2,3) Sub-Riemannian Manifolds
Daniel R. Cole
We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties o…
math.DG2004★ 16 cited
C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable
Daniel R. Cole, Scott D. Pauls
We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable,…