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math.DG2025
Not all sub-Riemannian minimizing geodesics are smooth
Yacine Chitour, Frédéric Jean, Roberto Monti +4
A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an exa…
math.DG2015
Horizontal holonomy and foliated manifolds
Y. Chitour, E. Grong, F. Jean +1
We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle of the tangent bundle. We provide expl…