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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Real submanifolds of codimension two in complex manifolds


Author: Hon Fei Lai
Journal: Trans. Amer. Math. Soc. 264 (1981), 331-352
MSC: Primary 53B35
MathSciNet review: 603767
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Abstract: The equivalence problem for a real submanifold $ M$ of dimension at least eight and codimension two in a complex manifold is solved under a certain nondegeneracy condition on the Levi form. If the Levi forms at all points of $ M$ are equivalent, a normalized Cartan connection can be defined on a certain principal bundle over $ M$. The group of this bundle can be described by means of the osculating quartic of $ M$ or the prolongation of the graded Lie algebra of type $ {\mathfrak{g}_2} \oplus {\mathfrak{g}_1}$ defined by the Levi form.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0603767-5
PII: S 0002-9947(1981)0603767-5
Keywords: Pseudoconformal invariants, Levi form, prolongation of graded Lie algebras, Cartan connection
Article copyright: © Copyright 1981 American Mathematical Society