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Real analytic manifolds in n with parabolic complex tangents along a submanifold of codimension one

Patrick Ahern, Xianghong Gong (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We will classify n -dimensional real submanifolds in n which have a set of parabolic complex tangents of real dimension n - 1 . All such submanifolds are equivalent under formal biholomorphisms. We will show that the equivalence classes under convergent local biholomorphisms form a moduli space of infinite dimension. We will also show that there exists an n -dimensional submanifold M in n such that its images under biholomorphisms ( z 1 , , z n ) ( r z 1 , , r z n - 1 , r 2 z n ) , r > 1 , are not equivalent to M via any local volume-preserving holomorphic...

Regular holomorphic images of balls

John Erik Fornaess, Edgar Lee Stout (1982)

Annales de l'institut Fourier

Every n -dimensional complex manifold (connected, paracompact and Hausdorff) is the image of the unit ball in C n under a finite holomorphic map that is locally biholomorphic.

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