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Paper IPM / M / 15518  


Abstract:  
Applying Elie Cartanï¿½??s classical method, we show that the biholomorphic equivalence problem
to a totally nondegenerate Beloshapkaï¿½??s model of CR dimension one and codimension k > 1, whence of real
dimension 2 + k, is reducible to some absolute parallelism, namely to an estructure on a certain prolonged
manifold of real dimension either 3 + k or 4 + k. The proof relies upon a weight analysis on the structure
equations associated with the mentioned problem of equivalence. As a consequence of the achieved results, we
also confirm in CR dimension one Beloshapkaï¿½??s maximum conjecture on the rigidity of his models of certain
lengths equal or greater than three.
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