Real submanifolds of codimension two in complex manifolds

Lai, Hon Fei

doi:10.1090/S0002-9947-1981-0603767-5

Real submanifolds of codimension two in complex manifolds
HTML articles powered by AMS MathViewer

by Hon Fei Lai PDF

Trans. Amer. Math. Soc. 264 (1981), 331-352 Request permission

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.

References

D. Burns Jr. and S. Shnider, Pseudoconformal geometry of hypersurfaces in $C^{n}+^{1}$, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 2433–2436. MR 382727, DOI 10.1073/pnas.72.6.2433
S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
Robert Hermann, Convexity and pseudoconvexity for complex manifolds, J. Math. Mech. 13 (1964), 667–672. MR 0167995
Shôshichi Kobayashi, On connections of Cartan, Canadian J. Math. 8 (1956), 145–156. MR 77978, DOI 10.4153/CJM-1956-018-8
Hon Fei Lai, Characteristic classes of real manifolds immersed in complex manifolds, Trans. Amer. Math. Soc. 172 (1972), 1–33. MR 314066, DOI 10.1090/S0002-9947-1972-0314066-8
Noboru Tanaka, On the pseudo-conformal geometry of hypersurfaces of the space of $n$ complex variables, J. Math. Soc. Japan 14 (1962), 397–429. MR 145555, DOI 10.2969/jmsj/01440397
Noboru Tanaka, On generalized graded Lie algebras and geometric structures. I, J. Math. Soc. Japan 19 (1967), 215–254. MR 221418, DOI 10.2969/jmsj/01920215
Noboru Tanaka, On differential systems, graded Lie algebras and pseudogroups, J. Math. Kyoto Univ. 10 (1970), 1–82. MR 266258, DOI 10.1215/kjm/1250523814