Chapter

Real Methods in Complex and CR Geometry

Volume 1848 of the series Lecture Notes in Mathematics pp 109-163

Date:

Local Equivalence Problems for Real Submanifolds in Complex Spaces

  • Xiaojun HuangAffiliated withDepartment of Mathematics, Rutgers University Email author 

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Contents.

  • 1. Global and Local Equivalence Problems

  • 2. Formal Theory for Levi Non-degenerate Real Hypersurfaces
    • 2.1. General Theory for Formal Hypersurfaces

    • 2.2. \( {\cal H}_k\)-Space and Hypersurfaces in the \( {\cal H}_k\)-Normal Form

    • 2.3. Application to the Rigidity and Non-embeddability Problems

    • 2.4. Chern-Moser Normal Space \({\cal N}_{CH}\)

  • 3. Bishop Surfaces with Vanishing Bishop Invariants
    • 3.1. Formal Theory for Bishop Surfaces with Vanishing Bishop Invariant

  • 4. Moser-Webster’s Theory on Bishop Surfaces with Non-exceptional Bishop Invariants
    • 4.1. Complexification \({\cal M}\) of M and a Pair of Involutions Associated with \({\cal M}\)

    • 4.2. Linear Theory of a Pair of Involutions Intertwined by a Conjugate Holomorphic Involution

    • 4.3. General Theory on the Involutions and the Moser-Webster Normal Form

  • 5. Geometric Method to the Study of Local Equivalence Problems
    • 5.1. Cartan’s Theory on the Equivalent Problem

    • 5.2. Segre Family of Real Analytic Hypersurfaces

    • 5.3. Cartan-Chern-Moser Theory for Germs of Strongly Pseudoconvex Hypersurfaces

  • References

Mathematics Subject Classification (2000):

32V05 32V40 32A40 32H50 32VB25 32V35