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Covariant derivative

Ciro Santilli (@cirosantilli, 37) Mathematics Area of mathematics Calculus Topology Manifold
Updated 2025-07-16  1 By others on same topic  0 Discussions Create my own version
A generalized definition of derivative that works on manifolds.
TODO: how does it maintain a single value even across different coordinate charts?

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Covariant derivative by Wikipedia Bot 0
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The covariant derivative is a way to differentiate vector fields and tensor fields in a manner that respects the geometric structure of the underlying manifold. It is a generalization of the concept of directional derivatives from vector calculus to curved spaces, ensuring that the differentiation has a consistent and meaningful geometric interpretation. ### Key Concepts: 1. **Manifold**: A manifold is a mathematical space that locally resembles Euclidean space and allows for the generalization of calculus in curved spaces.
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