Warped products refer to a specific type of Riemannian manifold constructed from two manifolds where one is 'warped' by a smooth function defined on the other. This concept allows for the combination of different geometric structures, enabling the exploration of more complex manifold properties. Warped products are crucial in understanding the geometry of Riemannian submersions and play an important role in O'Neill's formulas, which relate the geometry of submanifolds to their ambient spaces.
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