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In this paper, we present the general analytic solution to the zero curvature equation for rigid three-dimensional CR-manifolds. The solutions are uniquely determined by one function and four real parameters. 相似文献
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We study some remarkable classes of metric f-structures on differentiable manifolds (namely, almost Hermitian, almost contact, almost S-structures and K-structures). We state and prove the necessary condition(s) for the existence of maps commuting such structures. The paper contains several new results, of geometric significance, on CR-integrable manifolds and the harmonicity of such maps. 相似文献
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In our recent work, we showed that C∞ CR-diffeomorphisms of real-analytic Levi-nonflat hypersurfaces in ?2 are not analytic in general. This result raised again the question on the nature of CR-maps of a real-analytic hypersurfaces.In this paper, we give a complete picture of what CR-maps actually are. First, we discover an analytic continuation phenomenon for CR-diffeomorphisms which we call the sectorial analyticity property. It appears to be the optimal regularity property for CR-diffeomorphisms in general. We emphasize that such type of extension never appeared previously in the literature. Second, we introduce the class of Fuchsian type hypersurfaces and prove that (infinitesimal generators of) CR-automorphisms of a Fuchsian type hypersurface are still analytic. In particular, this solves a problem formulated earlier by Shafikov and the first author.Finally, we prove a regularity result for formal CR-automorphisms of Fuchsian type hypersurfaces. 相似文献
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V.K. Beloshapka 《Journal of Mathematical Analysis and Applications》2011,374(2):655-672
Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E. Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us also to classify all symmetric CR-manifolds in dimension 4, up to local CR-equivalence. 相似文献
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In this paper, we study the class of almost contact metric manifolds which are conformal to Trans-Sasakian manifolds, and we construct concrete examples from almost Hermitian manifolds using the product of manifolds. As a consequence, we obtain several properties for the three-dimensional case. 相似文献
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