Schwarzian derivatives for pluriharmonic mappings

A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in Cn are introduced. Basic properties such as the chain rule, multiplicative invariance affine proved these operators. It is shown that stable only with respect to rotations of identity. characterization given case when holomorphic. Furthermore, it if mapping vanishes then analytic part this Möbius transformation. Some observations made related dilatation their transformations, revealing differences between theories plane higher dimensions. An example rules out possibility shear construction theorem hold Cn, n≥2.