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

Authors: Patrick Ahern; Xianghong Gong;

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

Abstract

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Average
Average
gold