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An object named for this mathematician transforms with conformal metric changes by adding two derivative terms and subtracting an inner product times the gradient. In orbital mechanics, this mathematician names the 2D case of a regularization scheme accomplished with the Kustaanheimo–Stiefel transformation. Parallelograms in curved spaces are named for this formulator of the notion of parallel transport. (15[1]-5[1])The fundamental theorem of Riemannian geometry asserts the existence of a natural (*) connection named (-5[1])for (10[1])this mathematician, (10[2])which is torsion-free (10[2])and compatible (10[1])with the metric. The Leibniz formula for the determinant is most compactly written as a sum with coefficients given by a pseudo-tensor named for this mathematician, which takes the value plus one, minus one, or zero depending on the parity of a permutation. For 10 points, name this Italian differential (-5[1])geometer and namesake of a “symbol” denoted epsilon. ■END■ (10[4]0[3])

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