 Symmetry of the second fundamental form

ID: symmetry-of-the-second-fundamental-form

Codex  0 Created 2026-09-24 Updated 2026-09-24

The second fundamental form is symmetric because the ambient Euclidean connection is torsion-free:

A (X, Y) - A (Y, X) = (\overline{\nabla}_{X} Y - \overline{\nabla}_{Y} X - [X, Y])^{⊥} = 0.

 New to topics? Read the docs here!