Local geometric properties of real submanifolds in complex space

By M. S. Baouendi, P. Ebenfelt, Linda Preiss Rothschild. 2000

83 citations recorded by the source corpus.

We survey some recent results on local geometric properties of real submanifolds of complex space. Our main focus is on the structure and properties of mappings between such submanifolds. We relate these results to the classification of real submanifolds under biholomorphic, algebraic, or formal transformations. Examples and open problems in this context are also mentioned.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/217823d2e93a48cc7e8879cc039080ee9240dd9a

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Reflection Ideals and mappings between generic submanifolds in complex space (2000, background): “A related question for real-algebraic submanifolds is the following, which has been asked in [4]: If two germs of real-algebraic submanifolds are biholomorphically equivalent, are they also algebraically equivalent? It is shown in [13] that at “general” points the answer is positive.”
A Bishop surface with a vanishing Bishop invariant (2007, background): “Just to name a few, we here mention the work in [2,20,24,25] and the references therein.”
The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics (2002, background): “(1.6) below or [ BER00 ] for an explicit formula).”
Equivalence and embedding problems for CR-structures of any codimension (2001, unknown): “1”