On Invariants of Immersions of an <i>n</i>-Dimensional Manifold in an <i>n</i>-Dimensional Pseudo-Euclidean Space*

Let E n p be the n-dimensional pseudo-Euclidean space of index p and M (n, p) the group of all transformations of E n p generated by pseudo-orthogonal transformations and parallel translations. We describe the system of generators of the differential field of all M (n, p)-invariant differential rational functions of a map x : J E n p of an open subset J E n p . Using this result, we prove analogues of the Bonnet theorem for immersions of an n-dimensional C -manifold J in E n p . These analogues are given in terms of the pseudo-Riemannian metric, the volume form, and the connection on J induced by the immersion of J in E n p .

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