
doi: 10.5802/afst.1204
We will classify n -dimensional real submanifolds in ℂ 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 ℂ 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 map.
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