Abstract CR−submanifolds of a kahlerian manifold have been defined by A. Bejancu[1], and are now being studied by various authors, see [2] and [3]. The theory of F−structure was devolped by Yano [4], Yano and Ishihara [5], Goldberg [6] and among others. The purpose of this paper is to show a relationship between CR−structures and F−structure satisfying F 2K+P + FP = 0, where K is a fixed intege...

We study a germ of real analytic n-dimensional submanifold of C that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions, we show its equivalence to a normal form under a local biholomorphism at the singularity. We also show that if a real submanifold is formally equivalent to a quadric, it is actually holomorphically equivalent to it, if a small divisor...

We prove that for an induced CR structure on a compact, generic, regular 3-pseudoconcave CR submanifold M ⊂ G, of a complex manifold G, satisfying condition dimH1 ( M, T ′(G)| M ) = 0 all the close CR structures are induced by close embeddings.

We survey some recent results on holomorphic or formal mappings sending real submanifolds into each other in complex space.

Let E be a generic real submanifold of an almost complex manifold. The geometry of Bishop discs attached to E is studied in terms of the Levi form of E. Résumé. Nous étudions la géométrie des disques de Bishop attachés à une sous-variété réelle générique d’une variété presque complexe. MSC: 32H02, 53C15.