Geodesic
A~Quasiperiodic System of Polynomial Models of CR-Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 7-35.

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Polynomial models for the germs of real submanifolds of a complex space are constructed. For the germs whose Levi–Tanaka algebra has length 2, such a sufficiently well-studied model is given by a tangent quadric. It is shown that models of the third and fourth degrees (algebras of lengths 3 and 4) possess, in their codimension ranges, a full spectrum of properties that are completely analogous to the properties of tangent quadrics. For the constructed higher order models, a full spectrum of properties is obtained with the only exception that they are not fully universal. 
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V. K. Beloshapka. A~Quasiperiodic System of Polynomial Models of CR-Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 7-35. http://geodesic.mathdoc.fr/item/TM_2001_235_a0/

[1] Beloshapka V. K., “Konechnomernost gruppy avtomorfizmov veschestvenno analiticheskoi poverkhnosti”, Izv. AN SSSR. Ser. mat., 52:2 (1988), 437–442 | MR | Zbl

[2] Beloshapka V. K., “O golomorfnykh preobrazovaniyakh kvadriki”, Mat. sb., 182:2 (1991), 203–219 | MR | Zbl

[3] Beloshapka V. K., “Kubicheskaya model veschestvennogo mnogoobraziya”, Mat. zametki, 70:4 (2001), 503–519 | 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] Palamodov V. P., Lineinye differentsialnye operatory s postoyannymi koeffitsientami, Nauka, M., 1967 | MR

[6] Tumanov A. E., “Konechnomernost gruppy {CR}-avtomorfizmov standartnogo {CR}-mnogoobraziya i sobstvennye golomorfnye otobrazheniya oblastei Zigelya”, Izv. AN SSSR, 52:3 (1988), 651–659 | MR | Zbl

[7] Chirka E. M., “Vvedenie v geometriyu {CR}-mnogoobrazii”, UMN, 46:1 (1991), 81–164 | MR | Zbl

[8] Shananina E. N., “Modeli {CR}-mnogoobrazii tipa $(1,k)$ pri $3\leqslant k\leqslant 7$ i ikh avtomorfizmy”, Mat. zametki, 67:3 (2000), 452–459 | MR | Zbl

[9] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Kn. 2, Nauka, M., 1972, 183 pp. | MR

[10] Baouendi M. S., Ebenfelt P., Rothschild L. P., Local gometric properties of real submanifolds in complex space, Preprint Trita-Mat-1999-20, Roy. Inst. Technology, Stockholm, Sweden, 1999 | MR

[11] Chern S. S., Moser J. K., “Real hypersurfaces in complex manifold”, Acta Math., 133:3–4 (1974), 219–271 | DOI | MR

[12] Ezhov V., Schmalz G., “Infinitezimale Starrheit hermitescher Quadriken in allgemeiner Lage”, Math. Nachr., 204 (1999), 41–60 | MR | Zbl

[13] Naruki I., “Holomorphic extension problem for standart real submanifolds of second kind”, Publ. Res. Inst. Math. Kioto Univ., 6:1 (1970), 113–187 | DOI | MR | Zbl

[14] Tanaka N., “On the pseudo-conformal geometry of hypersurfaces of the space of $n$ complex variables”, J. Math. Soc. Japan, 14 (1962), 397–429 | DOI | MR | Zbl

[15] Tanaka N., “Graded Lie algebras and geometric structures”, Proc. US–Japan Seminar in Differential Geometry, Nippon Hyoronsha, Tokyo, 1965, 147–150 | MR