Stability of the Vanishing of the $$ \bar \partial _b $$ -cohomoloy Under Small Horizontal Perturbations of the CR Structure in Compact Abstract q-concave CR Manifolds

2010 ◽  
pp. 213-225
Author(s):  
Christine Laurent-Thiébaut
Keyword(s):  
Cr Manifolds ◽  
Cr Structure

STATIONARY DISCS AND GEOMETRY OF CR MANIFOLDS OF CODIMENSION TWO

2001 ◽  
Vol 12 (08) ◽  
pp. 877-890 ◽  
Author(s):  
A. SUKHOV ◽  
A. TUMANOV
Keyword(s):  
Contact Structure ◽  
Cr Manifolds ◽  
Codimension Two ◽  
Strictly Convex ◽  
Cr Structure ◽  
Conormal Bundle ◽  
Convex Hypersurfaces

We give a construction of stationary discs and the indicatrix for manifolds of higher codimension which is a partial analog of L. Lempert's theory of stationary discs for strictly convex hypersurfaces. This leads to new invariants of the CR structure in higher codimension linked with the contact structure of the conormal bundle.

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.

scholarly journals CR embeddability of quotients of the Rossi sphere via spectral theory

2022 ◽  
Author(s):  
Henry Bosch ◽  
Tyler Gonzales ◽  
Kamryn Spinelli ◽  
Gabe Udell ◽  
Yunus E. Zeytuncu
Keyword(s):  
Asymptotic Distribution ◽  
Spectral Theory ◽  
Unit Sphere ◽  
Point Spectrum ◽  
Cr Manifold ◽  
Cr Manifolds ◽  
Cr Structure ◽  
Finite Subgroups

We look at the action of finite subgroups of SU(2) on [Formula: see text], viewed as a CR manifold, both with the standard CR structure as the unit sphere in [Formula: see text] and with a perturbed CR structure known as the Rossi sphere. We show that quotient manifolds from these actions are indeed CR manifolds, and relate the order of the subgroup of SU(2) to the asymptotic distribution of the Kohn Laplacian’s eigenvalues on the quotient. We show that the order of the subgroup determines whether the quotient of the Rossi sphere by the action of that subgroup is CR embeddable. Finally, in the unperturbed case, we prove that we can determine the size of the subgroup by using the point spectrum.

scholarly journals Classification of Levi degenerate homogeneous CR-manifolds in dimension 5

2008 ◽  
Vol 201 (1) ◽  
pp. 1-82 ◽  
Author(s):  
Gregor Fels ◽  
Wilhelm Kaup
Keyword(s):  
Cr Manifolds ◽  
Homogeneous Cr Manifolds

scholarly journals A parametrized de Rham decomposition theorem for CR manifolds

2014 ◽  
Vol 66 (1) ◽  
pp. 93-105
Author(s):  
Atsushi Hayashimoto
Keyword(s):  
Decomposition Theorem ◽  
Cr Manifolds ◽  
De Rham

On the standard nondegenerate almost CR structure of tangent hyperquadric bundles

2016 ◽  
Vol 185 (1) ◽  
pp. 15-33 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Cr Structure
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