Lie contact structures and normal Cartan connections
Let N be a (2n-1)-dimensional differentiable manifold. A Lie contact structure on N is defined to be a certain special reduction of the linear frame bundle over N [\textit{H. Sato} and \textit{K. Yamaguchi}, Geometry of manifolds, Coll. Pap. 35th Symp. Differ. Geom., Matsumoto/Japan 1988, Perspect. Math. 8, 191-238 (1989; Zbl 0705.53019)]. One of the important examples of such structures is that given on the unit tangent bundle \(T_ 1M\) of a Riemannian manifold M. Following the connection theory by \textit{N. Tanaka} [Hokkaido Math. J. 8, 23-84 (1979; Zbl 0409.17013)], the author constructs a normal Cartan connection (so-called Tanaka connection) corresponding to a Lie contact structure. Next, he proves that the normal connection determines the structure completely.
scientific article; zbMATH DE number 4210971