Geodesic
Vitushkin's Germ Theorem for Engel-Type CR Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 7-13

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We study real analytic CR manifolds of CR dimension $1$ and codimension $2$ in the three-dimensional complex space. We prove that the germ of a holomorphic mapping between “nonspherical” manifolds can be extended along any path (this is an analog of Vitushkin's germ theorem). For a cubic model surface (“sphere”), we prove an analog of the Poincaré theorem on the mappings of spheres into $\mathbb~C^2$. We construct an example of a compact “spherical” submanifold in a compact complex $3$-space such that the germ of a mapping of the “sphere” into this submanifold cannot be extended to a certain point of the “sphere.” 
@article{TM_2006_253_a0,
     author = {V. K. Beloshapka and V. V. Ezhov and G. Schmalz},
     title = {Vitushkin's {Germ} {Theorem} for {Engel-Type} {CR} {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {7--13},
     publisher = {mathdoc},
     volume = {253},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_253_a0/}
}
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V. K. Beloshapka; V. V. Ezhov; G. Schmalz. Vitushkin's Germ Theorem for Engel-Type CR Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis and applications, Tome 253 (2006), pp. 7-13. http://geodesic.mathdoc.fr/item/TM_2006_253_a0/