Regular type of real hyper-surfaces in (almost) complex manifolds

J. -F. Barraud (1) , E. Mazzilli (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

The regular type of a real hyper-surface M in an (almost) complex manifold at some point p is the maximal contact order at p of M with germs of non singular (pseudo) holomorphic disks. The main purpose of this paper is to give two intrinsic characterizations the type: one in terms of Lie brackets of a complex tangent vector field on M, the other in terms of some kind of derivatives of the Levi form.

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

J. -F. Barraud, E. Mazzilli. Regular type of real hyper-surfaces in (almost) complex manifolds. Mathematische Zeitschrift, 2004, 248, No.4, pp.757-772. ⟨hal-00014125⟩