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Transactions of the American Mathematical Society

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Local and infinitesimal rigidity of hypersurface embeddings


Authors: Giuseppe della Sala, Bernhard Lamel and Michael Reiter
Journal: Trans. Amer. Math. Soc. 369 (2017), 7829-7860
MSC (2010): Primary 32H02, 32V40
DOI: https://doi.org/10.1090/tran/6885
Published electronically: May 1, 2017
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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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Additional Information

Giuseppe della Sala
Affiliation: Fakultät für Mathematik, Universität Wien, Vienna, Austria
Address at time of publication: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: gd16@aub.edu.lb

Bernhard Lamel
Affiliation: Fakultät für Mathematik, Universität Wien, Vienna, Austria
Email: bernhard.lamel@univie.ac.at

Michael Reiter
Affiliation: Fakultät für Mathematik, Universität Wien, Vienna, Austria
Email: m.reiter@univie.ac.at

DOI: https://doi.org/10.1090/tran/6885
Received by editor(s): March 5, 2015
Received by editor(s) in revised form: November 25, 2015
Published electronically: May 1, 2017
Additional Notes: The first author would like to thank the Center for Advanced Mathematical Sciences (CAMS) at AUB
The second author was supported by the FWF-Project I382 and QNRF-Project NPRP 7-511-1-098
The third author was supported by the FWF-Project P28873
Article copyright: © Copyright 2017 American Mathematical Society

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