Affine Connections and Defining Functions of Real Hypersurfaces in C n

An explicit formula for the Webster pseudo-Ricci curvature on real hypersurfaces and its application for characterizing balls in {$\Bbb C\sp n$}

“…In particular, if there is a non-vanishing holomorphic (n + 1)-form on M , then M is pseudo-Einstein, which includes the boundary of strictly pseudo-convex domain in C n+1 . In fact, the last result was obtained earlier by Luk in [27]. He showed that the boundary of any smoothly bounded strictly pseudo-convex domain D = {ρ(z) < 0} with the contact form θ = (−i/2)(∂ρ − ∂ρ) generated by the potential function ρ of the Fefferman metric is pseudo-Einstein.…”

An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its application to torsion-free hypersurfaces

“…Analysis and geometry on a strictly pseudoconvex pseudo-hermitian manifolds have been studied by many authors (see, for example, refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references therein). From geometric point of view, it is important to understand curvatures and torsion.…”