Hypersurfaces through higher-codimensional submanifolds of ?
n
with preserved Levi-kernelwith preserved Levi-kernel |
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Authors: | Giuseppe Zampieri |
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Institution: | (1) Dipartimento di Matematica, Università, v. Belzoni 7, 35131 Padova, Italy |
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Abstract: | For a “generic” submanifoldS of a complex manifoldX, we show that there exists a hypersurfaceM⊃S which has the same number of negative (or positive) Levi-eigenvalues asS at one prescribed conormal (cf. also 9]). When ranksL
S
is constant, thenM may be found such thatL
M
andL
S
have the same number of negative eigenvalues at any common conormal. Assuming the existence of a hypersurfaceM with the above property, we then discuss the link between complex submanifolds ofS whose tangent plane belongs to the null-space of the Levi-formL
S
ofS (of all complex submanifolds whenL
S
is semi-definite), and complex submanifolds ofT
S
*
X. As an application we give a simple result on propagation of microanalyticity for CR-hyperfunctions along complex,L
S
-null, curves (cf. 3]). |
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Keywords: | |
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