metric torsion

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• Torsion tensor — In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet Serret formulas, for instance, quantifies the twist of a curve… …   Wikipedia

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• Fundamental theorem of Riemannian geometry — In Riemannian geometry, the fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo Riemannian manifold) there is a unique torsion free metric connection, called the Levi Civita connection of the given metric …   Wikipedia

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• Connection form — In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan …   Wikipedia

• Levi-Civita connection — In Riemannian geometry, the Levi Civita connection is the torsion free Riemannian connection, i.e., the torsion free connection on the tangent bundle (an affine connection) preserving a given (pseudo )Riemannian metric.The fundamental theorem of… …   Wikipedia