Sunto
Data un’ipersuperficie differenziabileM di
si definisce lacurvatura di Levi k=k M diM. SeM è il grafico di una funzionex 4=u(x 1,x 2,x 3) (u∈C 2),u soddisfa un’equazione differenzialeL(k; u)=0 (dipendente dak) dettaequazione di Levi. Si dimostrano allora alcune proprietà geometriche delle soluzioni diL(k; u)=0.
Summary
For aC ∞-smooth real hypersurfaceM of
the Levi-curvaturek=k M is defined. IfM is the graph of aC 2-functionx 4=u(x 1,x 2,x 3) thenu is a solution of a differential equationL(k; u)=0 (depending onk) which is calledLevi-equation. Some geometric properties of the solutions ofL(k; u)=0 are then discussed.
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Bibliografia
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, Am. J. of Math. v. 105 (1983), 975–1009.Author information
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Tomassini, G. Proprieta’ geometriche delle soluzioni dell’equazione di Levi. Seminario Mat. e. Fis. di Milano 57, 103–108 (1987). https://doi.org/10.1007/BF02925044
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DOI: https://doi.org/10.1007/BF02925044