Non-solvability of the tangential -systems
- Volume: 9, Issue: 2, page 111-114
- ISSN: 1120-6330
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topZampieri, Giuseppe. "Non-solvability of the tangential \( \bar \partial_{M} \)-systems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.2 (1998): 111-114. <http://eudml.org/doc/252301>.
@article{Zampieri1998,
abstract = {We prove that for a real analytic generic submanifold \( M \) of \( \mathbb\{C\}^\{n\} \) whose Levi-form has constant rank, the tangential \( \bar \partial\_\{M\} \)-system is non-solvable in degrees equal to the numbers of positive and \( M \) negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with \( M \) non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.},
author = {Zampieri, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {CR manifolds; Tangential Cauchy-Riemann Complexes; Real/Complex symplectic structures; CR-manifolds; tangential Cauchy-Riemann complex; real/complex symplectic structures},
language = {eng},
month = {6},
number = {2},
pages = {111-114},
publisher = {Accademia Nazionale dei Lincei},
title = {Non-solvability of the tangential \( \bar \partial\_\{M\} \)-systems},
url = {http://eudml.org/doc/252301},
volume = {9},
year = {1998},
}
TY - JOUR
AU - Zampieri, Giuseppe
TI - Non-solvability of the tangential \( \bar \partial_{M} \)-systems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/6//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 2
SP - 111
EP - 114
AB - We prove that for a real analytic generic submanifold \( M \) of \( \mathbb{C}^{n} \) whose Levi-form has constant rank, the tangential \( \bar \partial_{M} \)-system is non-solvable in degrees equal to the numbers of positive and \( M \) negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with \( M \) non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.
LA - eng
KW - CR manifolds; Tangential Cauchy-Riemann Complexes; Real/Complex symplectic structures; CR-manifolds; tangential Cauchy-Riemann complex; real/complex symplectic structures
UR - http://eudml.org/doc/252301
ER -
References
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- Rea, C., Levi flat submanifolds and holomorphic extension of foliations. Ann. SNS Pisa, 26, 1972, 664-681. Zbl0272.57013MR425158
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- Zampieri, G., Microlocal complex foliation of -Lagrangian submanifolds. Tsukuba J. Math., 21 (1), 1997. Zbl0893.32008MR1473928
- Zampieri, G., Nonsolvability of the tangential -system in manifolds with constant Levi-rank. To appear. Zbl0967.32037
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