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ON INVARIANTS OF IMMERSIONS OF AN n-DIMENSIONAL MANIFOLD IN AN n-DIMENSIONAL PSEUDO-EUCLIDEAN SPACE

DJAVVAT KHADJIEV

Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey

https://doi.org/10.1142/S1402925110000799Cited by:6 (Source: Crossref)

Abstract

Let be the n-dimensional pseudo-Euclidean space of index p and M(n, p) the group of all transformations of 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 of an open subset . Using this result, we prove analogues of the Bonnet theorem for immersions of an n-dimensional C^∞-manifold J in . 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 .

This work was supported by the Research Fund of TUBITAK. Project number:107T049.

Keywords:

AMSC: Primary 53C50, Secondary 53B30, Secondary 53C24, Secondary 53C42

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