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Levi's forms of higher codimensional submanifolds

Andrea D'Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X 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 S . In a previous paper [3] two numbers s ± S , p , p T ˙ S * X z 0 are defined; for S = M they are the numbers of positive and negative eigenvalues for L M . For S M , p S × M T ˙ * S X ) , we show here that s ± S , p are still the numbers of positive and negative eigenvalues for L M when restricted to T z 0 C S . Applications to the concentration in degree for microfunctions at the boundary are given.

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