On the existence of local quaternionic contact geometries

2017/11/26 by Ivan Minchev, Minchev, Ivan, Jan Slovák +1
Mathematics · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1711.09420

openalex publication_date 2017/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exploit the Cartan-Kähler 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.

Citations

• Notes on exterior differential systems
• Quaternionic contact Einstein structures and the quaternionic contact Yamabe problem

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