In
mathematics,
curvature is any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being
flat, or
straight in the case of a
line, but this is defined in different ways depending on the context. There is a key distinction between
extrinsic curvature, which is defined for objects embedded in another space (usually a
Euclidean space) in a way that relates to the
radius of curvature of circles that touch the object, and
intrinsic curvature, which is defined at each point in a
Riemannian manifold. This article deals primarily with the first concept.