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What is the difference betweensub-Riemannianandcontact geometry?

User OCyril
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Final answer:

Sub-Riemannian geometry and contact geometry are both branches of mathematics that study different types of geometries. Sub-Riemannian geometry involves the constraints on the metric in a space, while contact geometry studies hypersurfaces called contact manifolds.

Step-by-step explanation:

Sub-Riemannian geometry studies the geometry of curves and surfaces in spaces where the metric is constrained by a set of vector fields. These vector fields define permissible directions of motion at each point, leading to a non-Euclidean geometry. Contact geometry, on the other hand, studies the geometry of hypersurfaces called contact manifolds, where each point is associated with a hyperplane called the contact plane. This geometry is used to study physical phenomena such as friction and adhesion.

User HunterLion
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