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Second order differential invariants of linear frames. (English) Zbl 1220.53018

The aim of this paper is to characterize all second order tensor-valued and scalar differential invariants of the bundle of linear frames \(FX\) over an \(n\)-dimensional manifold \(X\). These differential invariants are obtained by factorization method and are described in terms of bases of invariants. Second order natural Lagrangians of frames have been characterized explicitly; if \(n=1, 2, 3, 4\), the number of functionally independent second order natural Lagrangians is \(N=0, 6, 33, 104\), respectively.
Reviewer: Radu Miron (Iaşi)

MSC:

53A55 Differential invariants (local theory), geometric objects
58A10 Differential forms in global analysis
58A20 Jets in global analysis
58A32 Natural bundles
16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras)
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