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Vitushkin’s germ theorem for engel-type CR manifolds |
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| Authors: | V. K. Beloshapka V. V. Ezhov G. Schmalz |
| Affiliation: | (1) Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia;(2) School of Mathematics and Statistics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA, 5095, Australia;(3) School of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW, 2351, Australia;(4) Wydział Matematyki-Informatyki, Uniwersytet Warmińsko-Mazurski, ul. Żołnierska 14, 10-561 Olsztyn, Poland |
| Abstract: | 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 ?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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