Riemannian Geometry
The Levi-Civita symbol is a mathematical object used in multilinear algebra and differential geometry, denoted by $$ ext{lev}(i_1, i_2, ext{...}, i_n)$$, where it takes values of 1, -1, or 0 depending on the permutation of its indices. It plays a crucial role in defining the orientation of a volume element in Riemannian geometry and is essential for operations like the cross product and determinants.
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