Differential geometry is a field of mathematics that uses techniques of calculus and algebra to study the properties and structures of geometric objects, particularly those that can be described by smooth curves and surfaces. It bridges the gap between algebraic geometry and classical geometry, allowing for the analysis of shapes through their curvature, connections, and other intrinsic features. This area of study is crucial when looking at submanifolds and embeddings, as it helps describe how these smaller spaces fit into larger geometric frameworks.
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