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Differential invariants of immersions of manifolds with metric fields. (English) Zbl 1066.58003

The main results of this article state that all \(r\)-order differential invariants depending on an immersion \(f: M\to N\) of smooth manifolds equipped with metric fields can be factorized through the metrics, the curvature tensors and their covariant differentials, up to order \(r-2\), and the covariant differentials of the tangent map \(Tf\), up to order \(r\).

MSC:

58A20 Jets in global analysis
53A55 Differential invariants (local theory), geometric objects
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