Analytic Discs Attached to Conormal Bundles of CR-Manifolds

✍ Scribed by Giuseppe Zampieri

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 304 KB
• Volume: 128
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1997.1636

✦ Synopsis

Let M be a CR-submanifold of X=C n , T * M X the conormal bundle to M in X,

a small analytic disc, C 1 up to the boundary, attached to M through z o , A* a lift of A to T*X through p o attached T * M X. If the Levi-form of M has a constant number of negative eigenvalues in a neighborhood of p 0 then we show that in fact A is contained in M and A* in T* M X. When M is a hypersurface and it is pseudoconvex (i.e., the number of its negative Levi-eigenvalues is identically 0), then the inclusion A/M is classical and follows from the Hopf Lemma applied to a plurisubharmonic exhaustion function as in [D-F]. Note that in this case the existence of a lift A*/T * M X is automatic according to [B-F]. 1980 Math. Subject Classification (1985 Revision): 32 F. 1997 Academic Press We denote by L M ( p o ) the Levi-form of M at p o , and by s & M ( p o ) the number of its negative eigenvalues. We assume that -&1p o  T* M X. It is then easy article no. AI971636 180