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Uspekhi Mat. Nauk, 2018, Volume 73, Issue 1(439), Pages 99–172 (Mi umn9788)  

Orthogonal complex structures in $\mathbb{R}^4$

E. M. Chirka

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Orthogonal complex structures in domains in $\mathbb{R}^4$ are studied using methods of multidimensional complex analysis. New results on removable singularities of such structures are established. The simplest multivalued orthogonal complex structures are investigated. A classification of quadrics in $\mathbb{CP}_3$ with respect to the action of the conformal group is given, and the discriminant sets of the twistor projections of model quadrics are described.
Bibliography: 39 titles.

Keywords: complex structures, conformal maps, twistor bundles, removable singularities, discriminant sets.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/rm9788

Full text: PDF file (978 kB)
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English version:
Russian Mathematical Surveys, 2018, 73:1, 91–159

Bibliographic databases:

Document Type: Article
UDC: 517.54+517.554+514.763.4
MSC: Primary 32Q60, 53C28; Secondary 53C15
Received: 08.08.2017

Citation: E. M. Chirka, “Orthogonal complex structures in $\mathbb{R}^4$”, Uspekhi Mat. Nauk, 73:1(439) (2018), 99–172; Russian Math. Surveys, 73:1 (2018), 91–159

Citation in format AMSBIB
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