The ambient Levi-Civita connection induces this metric connection on the normal bundle of an embedded submanifold. Its tangential counterpart appears in the Weingarten formula. Projecting the derivative preserves the connection on a vector bundle Leibniz rule and the fiber inner product.

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  1. Metric connection
  2. Connection (vector bundle)
  3. Vector bundle
  4. Fiber bundle
  5. Algebraic topology
  6. Geometry and topology
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