Sub-Riemannian geometry is a branch of differential geometry that studies the geometric properties of spaces equipped with a distribution of tangent spaces and a Riemannian metric defined only on these spaces. It focuses on the paths and structures that can be defined through the constraints of the distribution, allowing for the exploration of minimal geodesics and optimal control problems. This area has profound applications in fields like control theory and robotics, where navigating constrained environments is essential.
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