The Weyl tensor is a crucial mathematical construct in Riemannian geometry that measures the conformal curvature of a manifold. It represents the part of the curvature that describes how the shape of a manifold differs from flat space, independent of its local geometry. This tensor plays a vital role in understanding the structure of spacetime in general relativity, particularly in describing how the geometry can be deformed without affecting angles, which relates directly to the concept of conformal metrics.
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