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   Lloveras, D. G.; Vásquez, A. M.; Nuevo, F. A.; Frazin, R. A.; Manchester, W.; Sachdeva, N.; Van der Holst, B.; Lamy, P.; Gilardy, H. (June 2022, Journal of Geophysical Research: Space Physics)
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4. Obstruction flat rigidity of the CR 3-sphere

   https://doi.org/10.1515/crelle-2021-0051  

   Curry, Sean N.; Ebenfelt, Peter (October 2021, Journal für die reine und angewandte Mathematik (Crelles Journal))

   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. 

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5. The CR-Volume of Horizontal Submanifolds of Spheres

   https://doi.org/10.1093/imrn/rnaf044  

   Bernstein, Jacob; Bhattacharya, Arunima (March 2025, International Mathematics Research Notices)

   Abstract We study an analog in CR-geometry of the conformal volume of Li–Yau. In particular, to submanifolds of odd-dimensional spheres that are Legendrian or, more generally, horizontal with respect to the sphere’s standard CR-structure, we associate a quantity that is invariant under the CR-automorphisms of the sphere. We apply this concept to a corresponding notion of Willmore energy. 

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