Geodesic curvature refers to the measure of how a curve deviates from being a geodesic on a surface. It quantifies the bending of a curve relative to the surface itself, helping to describe how paths behave in curved spaces. This concept is important when analyzing geodesics, which are the shortest paths between points on a surface, as it connects geometric intuition with physical applications, such as understanding forces in physics and properties in differential geometry.
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