Projective connections in CR geometry

Holomorphic invariants of an analytic real hypersurface in ℂⁿ⁺¹ can be computed by several methods, coefficients of the Moser normal form [4], pseudo-con-formal curvature and its covariant derivatives [4], and projective curvature and its covariant derivatives [3]. The relation between these constructions is given in terms of reduction of the complex projective structure to a real form and exponentiation of complex vectorfields to give complex coordinate systems and corresponding Moser normal forms. Although the results hold for hypersurfaces with non-degenerate Levi-form, explicit formulas will be given only for the positive definite case.