Levi's forms of higher codimensional submanifolds

D'Agnolo, Andrea, and Zampieri, Giuseppe. "Levi's forms of higher codimensional submanifolds." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.1 (1991): 29-33. <http://eudml.org/doc/244271>.

@article{DAgnolo1991,
abstract = {Let \( X \cong C^\{n\} \), let \( M \) be a \( C^\{2\} \) hypersurface of \( X \), \( S \) be a \(C^\{2\} \) submanifold of \( M \). Denote by \( L\_\{M\}\) the Levi form of \( M \) at \( z\_\{0\} \in S \). In a previous paper [3] two numbers \( s^\{\pm\} (S,p)\), \( p \in (\dot\{T\}^\{*\}\_\{S\}X)\_\{z\_\{0\}\} \) are defined; for \( S = M \) they are the numbers of positive and negative eigenvalues for \( L\_\{M\} \). For \( S \subset M \), \( p \in S \times\_\{M\} \dot\{T\}^\{*\}\_\{S\}X) \), we show here that \( s^\{\pm\} (S, p) \) are still the numbers of positive and negative eigenvalues for \( L\_\{M\} \) when restricted to \( T^\{C\}\_\{z\_\{0\}\}S \). Applications to the concentration in degree for microfunctions at the boundary are given.},
author = {D'Agnolo, Andrea, Zampieri, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Partial differential equations on manifolds; Boundary value problems; Theory of functions; PDE on manifolds; boundary value problem; Levi form of submanifold},
language = {eng},
month = {3},
number = {1},
pages = {29-33},
publisher = {Accademia Nazionale dei Lincei},
title = {Levi's forms of higher codimensional submanifolds},
url = {http://eudml.org/doc/244271},
volume = {2},
year = {1991},
}

TY - JOUR
AU - D'Agnolo, Andrea
AU - Zampieri, Giuseppe
TI - Levi's forms of higher codimensional submanifolds
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/3//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 1
SP - 29
EP - 33
AB - Let \( X \cong C^{n} \), let \( M \) be a \( C^{2} \) hypersurface of \( X \), \( S \) be a \(C^{2} \) submanifold of \( M \). Denote by \( L_{M}\) the Levi form of \( M \) at \( z_{0} \in S \). In a previous paper [3] two numbers \( s^{\pm} (S,p)\), \( p \in (\dot{T}^{*}_{S}X)_{z_{0}} \) are defined; for \( S = M \) they are the numbers of positive and negative eigenvalues for \( L_{M} \). For \( S \subset M \), \( p \in S \times_{M} \dot{T}^{*}_{S}X) \), we show here that \( s^{\pm} (S, p) \) are still the numbers of positive and negative eigenvalues for \( L_{M} \) when restricted to \( T^{C}_{z_{0}}S \). Applications to the concentration in degree for microfunctions at the boundary are given.
LA - eng
KW - Partial differential equations on manifolds; Boundary value problems; Theory of functions; PDE on manifolds; boundary value problem; Levi form of submanifold
UR - http://eudml.org/doc/244271
ER -