Lifts of Analytic Discs from X to T∗X
Vol. 5 (1998), No. 4, Page 713--725.
Baracco, Luca ; Zampieri, Giuseppe
Lifts of Analytic Discs from X to T∗X
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
We state a general criterion for existence of analytic discs attached to conormal bundles of CR manifolds. In particular let S be a CR (non--generic) submanifold of X=\Cn and E∗ a CR subbundle of the complex conormal bundle T∗SX∩\imT∗SX such that E∗+√−1E∗=T∗SX∩√−1T∗SX (where sum and multiplication by √−1 are understood in the sense of the fibers). We then show that for any small disc A attached to S through zo , and for any point po∈(E∗)zo, there is an analytic lift A∗ attached to E∗ through po. In particular we regain the theorem by Trepreau and Tumanov \cite{T 3} on existence of lifts for discs attached to non--minimal manifolds. Our criterion also applies to discs attached to manifolds with a constant number of negative Levi--eigenvalues. We finally state the uniqueness of small discs attached to (non--necessarily CR) manifolds M through a given point zo and with prescribed components in T\CzoM. This is a slight, but perhaps interesting, generalization of the classical result (often used all through this paper), on uniqueness of lifts of small discs attached to generic manifolds.
Mathematics Subject Classification (1991): 32F
Mathematical Reviews Number: MR1675244
Received: 1997-04-17
