👉 Pulling math is a fundamental concept in differential geometry that describes how to compare the intrinsic geometry of a manifold by studying its extrinsic properties, specifically how it sits within a higher-dimensional space. It involves the use of tensors, particularly the first and second fundamental forms, to quantify how a surface or manifold curves within that space. The key idea is to measure the intrinsic curvature of the manifold by examining how it stretches or bends when embedded in a higher-dimensional ambient space. The "pulling" comes from projecting the intrinsic curvature onto this ambient space, allowing us to understand how the manifold's shape is influenced by its embedding. This process is crucial for applications in general relativity, where the geometry of spacetime is often studied both intrinsically and extrinsically.
