Decomposition of derivatives and compatibility conditions (Q1816957)

Along a hypersurface \(\{x\in V_{N+1} |f(x)= 0\}\) in an \((N+1)\)-dimensional manifold \(V_{N+1}\), partial derivatives and covariant derivatives can be decomposed into ``inner derivatives'' (tangent to the hypersurface) and ``exterior derivatives'' (transverse to the hypersurface). In this paper a special scheme is presented that allows to perform this decomposition for arbitrarily high derivatives of tensor fields in a noniterative manner. The resulting formulae are particularly useful for the formulation of jump conditions of tensor fields which are regularly discontinuous along a hypersurface.