The Jacobian of classical tensor analysis is generalized to a transformation operator containing second derivatives. This operator and the Jacobian may be used to formulate a second order tensor calculus. In this calculus, a simple contraction scheme includes as special cases Lie differentiation, the Lie bracket, covariant differentiation, and differentiation with respect to the tensor connections of Bompiani.
Order Tensor Tensor Analysis Covariant Differentiation Transformation Operator Contraction Scheme
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