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The local equivalence problem in CR geometry. (English) Zbl 1164.32307
Summary: This article is dedicated to the centenary of the local CR equivalence problem, formulated by Henri Poincaré in 1907. The first part gives an account of Poincaré’s heuristic counting arguments, suggesting existence of infinitely many local CR invariants. Then we sketch the beautiful completion of Poincaré’s approach to the problem in the work of S. S. Chern and J. Moser on Levi nondegenerate hypersurfaces. The last part is an overview of recent progress in solving the problem on Levi degenerate manifolds.
MSC:
32V40 Real submanifolds in complex manifolds
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