New York Journal of Mathematics
Volume 26 (2020), 1093-1129


Ivan Minchev and Jan Slovák

On the existence of local quaternionic contact geometries

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Published: September 24, 2020.
Keywords: quaternionic contact, equivalence problem, Cartan connection, involution.
Subject: 53C15, 53C26, 53C30, 58J70.

We exploit the Cartan-Kahler theory to prove the local existence of real analytic quaternionic contact structures for any prescribed values of the respective curvature functions and their covariant derivatives at a given point on a manifold. We show that, in a certain sense, the different real analytic quaternionic contact geometries in 4n+3 dimensions depend, modulo diffeomorphisms, on 2n+2 real analytic functions of 2n+3 variables.


I.M. is partially supported by Contract DH/12/3/12.12.2017 and Contract 80-10-12/18.03.2020 with the Sofia University "St.Kl.Ohridski". J.S. is supported by the grant P201/12/G028 of the Grant Agency of the Czech Republic.

Author information

Ivan Minchev:
University of Sofia
Faculty of Mathematics and Informatics
blvd. James Bourchier 5, 1164 Sofia, Bulgaria


Jan Slovák:
Department of Mathematics and Statistics
Faculty of Science
Masaryk University
Kotlarska 2, 61137 Brno, Czech Republic