KnowraLevi-Civita connectionLinked fromLinked fromThe 11 pages that link to Levi-Civita connection, each with the reason it gives.All 11Broader topic 4Related 7Metric tensorRelated: It translates metric data into a rule for differentiating vector fields.Riemannian geometryRelated: It defines parallel transport and geodesics canonically from the metric.Covariant derivativeBroader topic: It is the standard choice of covariant derivative in Riemannian geometry.Riemann curvature tensorRelated: This is the standard connection used to obtain Riemannian curvature.Riemannian manifoldRelated: It defines parallel transport and geodesics in a way compatible with the metric.Christoffel symbolsRelated: Its coefficients are the Christoffel symbols most often computed in Riemannian geometry.Affine connectionBroader topic: It is the distinguished affine connection selected when a metric is supplied.Ricci curvatureRelated: Its curvature tensor supplies the quantity that is traced to obtain Ricci curvature.Tullio Levi-CivitaBroader topic: This construction bears his name and is the standard connection used in Riemannian geometry.Fundamental theorem of Riemannian geometryBroader topic: It is the connection whose existence and uniqueness the theorem asserts.Gauss's lemma (differential geometry)Related: Its geodesic equation and metric compatibility support the standard proof of the lemma.