580 research outputs found
Flexible and inflexible submanifolds
In this paper we prove new embedding results for compactly supported
deformations of submanifolds of : We show that if is
a -pseudoconcave submanifold of type in ,
then any compactly supported deformation stays in the space of globally
embeddable in manifolds. This improves an earlier
result, where was assumed to be a quadratic -pseudoconcave
submanifold of . We also give examples of weakly
-pseudoconcave manifolds admitting compactly supported
deformations that are not even locally embeddable.Comment: arXiv admin note: text overlap with arXiv:1611.0542
Non locally trivializable line bundles over compact Lorentzian manifolds
We consider compact manifolds of arbitrary codimension that satisfy
certain geometric conditions in terms of their Levi form. Over these compact
manifolds, we construct a deformation of the trivial line bundle over
which is topologically trivial over but fails to be even locally
trivializable over any open subset of . In particular, our results apply to
compact Lorentzian manifolds of hypersurface type.Comment: to appear in Annales de l'Institut Fourie
Remarks on weakly pseudoconvex boundaries: Erratum
We make two tiny corrections to our previous paper with the same title, and
also obtain, as a bonus, something new
On the Cauchy problem for the debar operator
We present new results concerning the solvability, of lack thereof, in the
Cauchy problem for the debar operator, with initial values assigned on a weakly
pseudoconvex hypersurface, and provide illustrative examples.Comment: This is the final version, which is appearing in Arkiv foer
Mathemati
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