DIFFERENTIAL GEOMETRY WARPED PRODUCT MANIFOLD & SUBMANIFOLD

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Warpped product manifolds are a key concept in both geometry and mathematical physics, particularly in general relativity. These manifolds feature a metric tensor that can be expressed as a Cartesian product, with the x-part being rescaled by a scalar function dependent on the y coordinates. This framework is crucial for understanding various solutions to the Einstein field equations, such as the Schwarzschild solution and Robertson-Walker models, highlighting their significance in the study of the universe's structure.