Obstruction flat rigidity of the CR 3-sphere
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Sean N. Curry
Abstract
We consider the obstruction flatness problem for small deformations of the standard CR 3-sphere. That rigidity holds for the CR sphere was previously known (in all dimensions) for the case of embeddable CR structures, where it also holds at the infinitesimal level. In the 3-dimensional case, however, a CR structure need not be embeddable. Unlike in the embeddable case, it turns out that in the nonembeddable case there is an infinite-dimensional space of solutions to the linearized obstruction flatness equation on the standard CR 3-sphere and this space defines a natural complement to the tangent space of the embeddable deformations. In spite of this, we show that the CR 3-sphere does not admit nontrivial obstruction flat deformations, embeddable or nonembeddable.
Funding statement: The second author was supported in part by the NSF grant DMS-1900955.
Acknowledgements
The authors would like to thank the anonymous referees for their careful reading and valuable comments that have helped to improve the presentation in this paper.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár
- Representation by sums of unlike powers
- Shortest closed curve to inspect a sphere
- Locally pro-p contraction groups are nilpotent
- Obstruction flat rigidity of the CR 3-sphere
- Rank functions on triangulated categories
- Local-global principles for homogeneous spaces over some two-dimensional geometric global fields
- VI-modules in non-describing characteristic, part II
- Extended Erratum to A parabolic flow toward solutions of the optimal transportation problem on domains with boundary (J. reine angew. Math. 672 (2012), 127–160)
Artikel in diesem Heft
- Frontmatter
- Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár
- Representation by sums of unlike powers
- Shortest closed curve to inspect a sphere
- Locally pro-p contraction groups are nilpotent
- Obstruction flat rigidity of the CR 3-sphere
- Rank functions on triangulated categories
- Local-global principles for homogeneous spaces over some two-dimensional geometric global fields
- VI-modules in non-describing characteristic, part II
- Extended Erratum to A parabolic flow toward solutions of the optimal transportation problem on domains with boundary (J. reine angew. Math. 672 (2012), 127–160)
