Levi-Civita connection for the metric on inherited from . Indeed, one can check that this connection preserves the metric. See also Weitzenböck connection Notes References See Volume I pag. 158 External links MathWorld: Levi-Civita Connection PlanetMath: Levi-Civita Connection Levi-Civita connection at the Manifold Atlas Riemannian geometry Connection (mathematics)