Gauss–Codazzi equations

In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Mainardi equations or Gauss–Peterson–Codazzi Formulas) are fundamental formulas which link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.

Gauss–Codazzi equations

In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Mainardi equations or Gauss–Peterson–Codazzi Formulas) are fundamental formulas which link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.