Local and infinitesimal rigidity of hypersurface embeddings

della Sala, Giuseppe; Lamel, Bernhard; Reiter, Michael

doi:10.1090/tran/6885

Local and infinitesimal rigidity of hypersurface embeddings
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by Giuseppe della Sala, Bernhard Lamel and Michael Reiter PDF

Trans. Amer. Math. Soc. 369 (2017), 7829-7860 Request permission

Abstract:

We study local rigidity properties of holomorphic embeddings of real hypersurfaces in $\mathbb {C}^2$ into real hypersurfaces in $\mathbb {C}^3$ and show that infinitesimal conditions imply actual local rigidity in a number of (important) cases. We use this to show that generic embeddings into a hyperquadric in $\mathbb {C}^3$ are locally rigid.

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