Semi-global Extension of Maximally Complex Submanifolds
نویسندگان
چکیده
Let A be a domain of the boundary of a strictly pseudoconvex domain Ω of Cn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain à of Ω, depending only on Ω and A, and a complex variety W ⊂ à such that bW ∩A = M . Moreover, a generalization to analytic sets of depth at least 4 is given.
منابع مشابه
Isotropic Lagrangian Submanifolds in Complex Space Forms
In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.
متن کاملUmbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms
We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...
متن کاملRicci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
متن کاملOptimal Inequalities for the Casorati Curvatures of Submanifolds in Generalized Space Forms Endowed with Semi-Symmetric Non-Metric Connections
Abstract: In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian space form with a semi-symmetric non-metric connection. Moreover, we show that in both cases, the equalities hold if and only if submani...
متن کاملB.y. Chen Inequalities for Bi-slant Submanifolds in Generalized Complex Space Forms
The aim of the present paper is to study Chen inequalities for slant, bi-slant and semi-slant submanifolds in generalized complex space forms.
متن کامل