A product manifold is a type of manifold formed by taking the Cartesian product of two or more manifolds, resulting in a new manifold that encapsulates the geometric and topological features of the original manifolds. This construction allows for the combination of various dimensions and structures, enabling the study of more complex geometries and their interactions. Product manifolds are foundational in Riemannian geometry, as they help illustrate how different manifolds can be combined while retaining their individual characteristics.
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