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.” 
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     author = {V. K. Beloshapka and V. V. Ezhov and G. Schmalz},
     title = {Vitushkin's {Germ} {Theorem} for {Engel-Type} {CR} {Manifolds}},
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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/

[1] Chern S.S., Moser J.K., “Real hypersurfaces in complex manifolds”, Acta math., 133 (1974), 219–271 | DOI | MR

[2] Poincaré H., “Les fonctions analytiques de deux variables et la représentation conforme”, Rend. Circ. Mat. Palermo, 23 (1907), 185–220 | DOI | Zbl

[3] Alexander H., “Holomorphic mappings from the ball and polydisk”, Math. Ann., 209:3 (1974), 249–256 | DOI | MR | Zbl

[4] Beloshapka V.K., “CR-varieties of the type $(1,2)$ as varieties of “super-high” codimension”, Russ. J. Math. Phys., 5:2 (1998), 399–404 | MR

[5] Beloshapka V.K., Ezhov V.V., Shmalts G., “Golomorfnaya klassifikatsiya chetyrekhmernykh poverkhnostei v $\mathbb C^3$”, Izv. RAN. Ser. mat. (to appear) | Zbl

[6] Beloshapka V., Ezhov V., Schmalz G., Canonical Cartan connection and holomorphic invariants on Engel CR manifolds, math.CV/0508084

[7] Vitushkin A.G., “Golomorfnye otobrazheniya i geometriya poverkhnostei”, Kompleksnyi analiz — mnogie peremennye — 1, Itogi nauki i tekhniki. Sovr. probl. matematiki. Fund. napr., 7, VINITI, M., 1985, 167–226 | MR

[8] Burns D., Jr., Shnider S., “Real hypersurfaces in complex manifolds”, Proc. Symp. Pure Math., 30 (1977), 141–168 | MR | Zbl

[9] Bedford E., Pinchuk S., “Domains in $\mathbb C^2$ with noncompact automorphism groups”, Indiana Univ. Math. J., 47:1 (1998), 199–222 | DOI | MR | Zbl

[10] Tanaka N., “On generalized graded Lie algebras and geometric structures. I”, J. Math. Soc. Japan, 19 (1967), 215–254 | DOI | MR | Zbl

[11] Engel F., “Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen”, Ber. Akad. Wiss. Leipzig, 41 (1889), 157–176