## Invariants of quadratic differential forms |

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2Fdudv algebraic forms algebraic invariants angle application arbitrary functions arsdxrdxs calculated Christoffel coefficients congruence consider const contravariant system coordinates corresponding covariant and contravariant covariant derivatives covariant differentiation covariant system deduce denote determined differential equations differential invariants differential parameters Edu2 element of length equations obtained equivalent symbols Euclidean space example expressed in terms finite follows form F functions f fundamental form Gaussian invariants geodesic curvature geometrical interpretation given gkhi Hence higher derivatives increments independent variables infinitesimal transformation invariant theory invariantive constituent invariants of order Jacobian linear transformation manifold Math method necessary and sufficient orthogonal ennuple orthogonal trajectories parametric curves particular plane quadratic differential form quadrilinear form quantities rank zero relations Riemann symbols satisfied second derivatives second order set of equations set of variables Similarly solution suppose surface system of order third derivatives trans