An object in differential geometry used to define the covariant derivative [1]. The Levi-Civita connection Open image in new window (also known as the symmetric Christoffel symbol ) is determined by two conditions, namely the covariant constancy of the metric Open image in new window and the absence of torsion Open image in new window . The Levi-Civita connection appears in Einstein’s theory of gravity based on the Equivalence Principle [2], but more general connections (with, for example, torsion [3]) may appear in certain supergravity theories [4].