Elementary Complex and CR Geometry

2021 ◽  
pp. 183-209
Author(s):  
John P. D’Angelo
Keyword(s):  
Cr Geometry

A Remark on Extensions of CR Functions from Hyperplanes

2008 ◽  
Vol 51 (1) ◽  
pp. 21-25
Author(s):  
Luca Baracco
Keyword(s):  
Radon Transform ◽  
Integral Geometry ◽  
Holomorphic Functions ◽  
Holomorphic Extension ◽  
General Statement ◽  
Cr Geometry ◽  
Cr Functions ◽  
Natural Context ◽  
Extension Of Functions

AbstractIn the characterization of the range of the Radon transform, one encounters the problem of the holomorphic extension of functions defined on ℝ2 \ Δℝ (where Δℝ is the diagonal in ℝ2) and which extend as “separately holomorphic” functions of their two arguments. In particular, these functions extend in fact to ℂ2 \ Δℂ where Δℂ is the complexification of Δℝ. We take this theorem from the integral geometry and put it in the more natural context of the CR geometry where it accepts an easier proof and amore general statement. In this new setting it becomes a variant of the celebrated “edge of the wedge” theorem of Ajrapetyan and Henkin.

scholarly journals The canonical Cartan bundle and connection in CR geometry

2009 ◽  
Vol 146 (2) ◽  
pp. 415-434 ◽  
Author(s):  
MARC HERZLICH
Keyword(s):  
Algebraic Approach ◽  
Geometric Description ◽  
Alternative Definition ◽  
Cr Geometry

AbstractWe give a simple differential geometric description of the canonical Cartan (or tractor) bundle and connection in CR geometry, thus offering an alternative definition to the usual abstract Lie algebraic approach.

scholarly journals An Obata-type theorem in CR geometry

2013 ◽  
Vol 95 (3) ◽  
pp. 483-502 ◽  
Author(s):  
Song-Ying Li ◽  
Xiaodong Wang
Keyword(s):  
Type Theorem ◽  
Cr Geometry

scholarly journals Chains in CR geometry as geodesics of a Kropina metric

2019 ◽  
Vol 350 ◽  
pp. 973-999 ◽  
Author(s):  
Jih-Hsin Cheng ◽  
Taiji Marugame ◽  
Vladimir S. Matveev ◽  
Richard Montgomery
Keyword(s):  
Cr Geometry
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