Embeddability of Some Three-Dimensional Weakly Pseudoconvex CR Structures

2004 ◽  
Vol 47 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Wei Wang
Keyword(s):  
Three Dimensional ◽  
Cr Structure ◽  
Weakly Pseudoconvex ◽  
Complex Ellipsoid ◽  
Cr Structures

AbstractWe prove that a class of perturbations of standard CR structure on the boundary of threedimensional complex ellipsoid Ep, q can be realized as hypersurfaces on ℂ2, which generalizes the result of Burns and Epstein on the embeddability of some perturbations of standard CR structure on S3.

scholarly journals Regularity of infinitesimal CR automorphisms

2016 ◽  
Vol 27 (14) ◽  
pp. 1650112 ◽  
Author(s):  
Stefan Fürdös ◽  
Bernhard Lamel
Keyword(s):  
Infinite Type ◽  
Cr Structure ◽  
Cr Structures ◽  
Infinitesimal Cr Automorphisms ◽  
Infinitesimal Automorphisms

We study the regularity of infinitesimal CR automorphisms of abstract CR structures which possess a certain microlocal extension and show that there are smooth multipliers, completely determined by the CR structure, such that if [Formula: see text] is such an infinitesimal CR automorphism, then [Formula: see text] is smooth for all multipliers [Formula: see text]. As an application, we study the regularity of infinitesimal automorphisms of certain infinite type hypersurfaces in [Formula: see text].

scholarly journals AV-Courant Algebroids and Generalized CR Structures

2011 ◽  
Vol 63 (4) ◽  
pp. 938-960 ◽  
Author(s):  
David Li-Bland
Keyword(s):  
Contact Structure ◽  
Complex Structures ◽  
Lie Algebroid ◽  
Courant Algebroids ◽  
The Third ◽  
Cr Structure ◽  
Generalized Complex Structures ◽  
Generalized Complex ◽  
Cr Structures

Abstract We construct a generalization of Courant algebroids that are classified by the third coho- mology group H3(A , V), where A is a Lie Algebroid, and V is an A-module. We see that both Courant algebroids and structures are examples of them. Finally we introduce generalized CR structures on a manifold, which are a generalization of generalized complex structures, and show that every CR structure and contact structure is an example of a generalized CR structure.

A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds

2018 ◽  
Vol 68 (5) ◽  
pp. 1129-1140
Author(s):  
Miroslava Antić
Keyword(s):  
Three Dimensional ◽  
Kähler Manifolds ◽  
Moving Frame ◽  
Kahler Manifolds ◽  
Twisted Product ◽  
Totally Geodesic ◽  
Cr Structure ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds ◽  
Cr Submanifolds

Abstract We investigate four-dimensional CR submanifolds in six-dimensional strict nearly Kähler manifolds. We construct a moving frame that nicely corresponds to their CR structure and use it to investigate CR submanifolds that admit a special type of doubly twisted product structure. Moreover, we single out a class of CR submanifolds containing this type of doubly twisted submanifolds. Further, in a particular case of the sphere $ \mathbb{S}^{6}(1) $, we show that the two families of four-dimensional CR submanifolds, those that admit a three-dimensional geodesic distribution and those ruled by totally geodesic spheres $ \mathbb{S}^{3} $ coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.

scholarly journals Contact Semi-Riemannian Structures in CR Geometry: Some Aspects

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 6 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Riemannian Manifolds ◽  
Integrability Condition ◽  
Cr Manifolds ◽  
Cr Geometry ◽  
Cr Structure ◽  
Cr Structures ◽  
Similarities And Differences ◽  
One To One ◽  
Riemannian Case

There is one-to-one correspondence between contact semi-Riemannian structures ( η , ξ , φ , g ) and non-degenerate almost CR structures ( H , ϑ , J ) . In general, a non-degenerate almost CR structure is not a CR structure, that is, in general the integrability condition for H 1 , 0 : = X - i J X , X ∈ H is not satisfied. In this paper we give a survey on some known results, with the addition of some new results, on the geometry of contact semi-Riemannian manifolds, also in the context of the geometry of Levi non-degenerate almost CR manifolds of hypersurface type, emphasizing similarities and differences with respect to the Riemannian case.

Partially integrable almost CR structures

2021 ◽  
Vol 8 (1) ◽  
pp. 403-414
Author(s):  
Takao Akahori
Keyword(s):  
Tangent Bundle ◽  
Deformation Theory ◽  
Contact Manifold ◽  
Point Of View ◽  
Cr Structure ◽  
Cr Structures ◽  
The Difference ◽  
Differential Manifold

Abstract Let (M, D) be a compact contact manifold with dim R M = 2n ≥ 5. This means that: M is a C ∞ differential manifold with dim R M = 2n ≥ 5. And D is a subbundle of the tangent bundle TM which satisfying; there is a real one form θ such that D = {X : X ∈ TM, θ(X) = 0}, and θ ^ Λ n−1(d ) ≠ 0 at every point of p of M. Especially, we assume that our D admits almost CR structure,(M, S). In this paper, inspired by the work of Matsumoto([M]), we study the difference of partially integrable almost CR structures from actual CR structures. And we discuss partially integrable almost CR structures from the point of view of the deformation theory of CR structures ([A1],[AGL]).

scholarly journals Obstruction flat rigidity of the CR 3-sphere

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sean N. Curry ◽  
Peter Ebenfelt
Keyword(s):  
Tangent Space ◽  
Dimensional Space ◽  
Dimensional Case ◽  
Infinite Dimensional Space ◽  
3 Dimensional ◽  
Infinite Dimensional ◽  
Cr Structure ◽  
Cr Structures ◽  
Small Deformations ◽  
Flatness Problem

Abstract We consider the obstruction flatness problem for small deformations of the standard CR 3-sphere. That rigidity holds for the CR sphere was previously known (in all dimensions) for the case of embeddable CR structures, where it also holds at the infinitesimal level. In the 3-dimensional case, however, a CR structure need not be embeddable. Unlike in the embeddable case, it turns out that in the nonembeddable case there is an infinite-dimensional space of solutions to the linearized obstruction flatness equation on the standard CR 3-sphere and this space defines a natural complement to the tangent space of the embeddable deformations. In spite of this, we show that the CR 3-sphere does not admit nontrivial obstruction flat deformations, embeddable or nonembeddable.

scholarly journals Modeling of plasmon resonance in periodic multilayer structures based on chromium with a surface island layer

2021 ◽  
pp. 26-32
Author(s):  
Ilya R. Koshelev ◽  
Asiya I. Mukhammad ◽  
Peter I. Gaiduk
Keyword(s):  
Time Domain ◽  
Plasmon Resonance ◽  
Finite Difference Time Domain ◽  
Absorption Peak ◽  
Multilayer Structures ◽  
Ir Detectors ◽  
Plasmon Absorption ◽  
Cr Structure ◽  
Cr Structures ◽  
Difference Time

The optical properties of Cr/Si/Cr and Cr/CrSi2 /Cr structures with periodically located chromium islands are modeled using the finite-difference time domain method. These structures are characterized by the phenomenon of plasmon resonance. The dependences of the intensity and position of the plasmon absorption peak on the thickness and radius of the islands are determined. It was observed that when the island thickness increases to 120 nm, the intensity of the absorption peak increases to 69 % for the Cr/Si/Cr structure and to 55 % for the Cr/CrSi2 /Cr structure. It was found that the peak of plasmon absorption in the spectrum of the Cr/Si/Cr structure is at a shorter wavelength (8.4 µm for Cr/Si/Cr, 11.1 µm for Cr/CrSi2/Cr), and also has a higher intensity (the share of absorbed radiation is 14 % higher compared to the peak of plasmon absorption in the spectrum of the Cr/CrSi2 /Cr structure). The obtained dependences indicate that the Cr/Si/Cr and Cr/CrSi2 /Cr structures can be used as IR detectors.

scholarly journals Extension of CR structures on three dimensional pseudoconvex CR manifolds

1998 ◽  
Vol 152 ◽  
pp. 97-129 ◽  
Author(s):  
Sanghyun Cho
Keyword(s):  
Finite Type ◽  
Complex Structure ◽  
Three Dimensional ◽  
Concave Side ◽  
Almost Complex Structure ◽  
Cr Manifolds ◽  
Almost Complex ◽  
Cr Structures ◽  
The Given

Abstract.Let be a smoothly bounded orientable pseudoconvex CR manifold of finite type and dimℝM = 3. Then we extend the given CR structure on M to an integrable almost complex structure on which is the concave side of M and M ⊂

CR-structures on three dimensional circle bundles

1992 ◽  
Vol 109 (1) ◽  
pp. 351-403 ◽  
Author(s):  
Charles L. Epstein
Keyword(s):  
Three Dimensional ◽  
Circle Bundles ◽  
Cr Structures
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