# On the equivalence of quaternionic contact structures

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## Abstract

Following the Cartan’s original method of equivalence supported by methods of parabolic geometry, we provide a complete solution for the equivalence problem of quaternionic contact structures, that is, the problem of finding a complete system of differential invariants for two quaternionic contact manifolds to be locally diffeomorphic. This includes an explicit construction of the corresponding Cartan geometry and detailed information on all curvature components.

## Keywords

Quaternionic contact Equivalence problem Cartan connection Involution## Mathematics Subject Classification

58G30 53C17## Notes

### Acknowledgements

I.M. is partially supported by Contract DFNI I02/4/12.12.2014 and Contract 80-10-33/2017 with the Sofia University “St.Kl.Ohridski”. I.M. is also supported by a SoMoPro II Fellowship which is cofunded by the European Commission (this article reflects only the author’s views, and the EU is not liable for any use that may be made of the information contained therein) from “People” specific program (Marie Curie Actions) within the EU Seventh Framework Program on the basis of the Grant Agreement REA No. 291782. It is further cofinanced by the South-Moravian Region. J.S. is supported by the Grant P201/12/G028 of the Grant Agency of the Czech Republic.

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