Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
Archives

On 4-quasiplanar mappings of semi-quaternion manifolds

##plugins.themes.bootstrap3.article.sidebar##

PDF (Русский)
Published Jan 20, 2017
DOI https://doi.org/10.15673/tmgc.v9i2.281

##plugins.themes.bootstrap3.article.main##

Irina Kurbatova
Odessa national University named after I. I. Mechnikov
http://orcid.org/0000-0003-0215-6060

Abstract

Earlier we entered a concept of the semi-quaternion structure on a manifold with affine connection generated by couple of almost complex structures. We also investigated 4-quasiplanar mappings of spaces with semi-quaternion structures under various conditions of differential character. In the present article studying of 4-quasiplanar mappings of semi-quaternion Kahlerian spaces continues. Geometrical objects, invariant concerning the considered mappings are under construction. The class of the semi-quaternion Kahlerian spaces admiting 4-quasiplanar mapping on flat space (4-quasiplane) is allocated. Their tensor sign is received. It is proved that any 4-quasiplane semi-quaternion Kahlerian space admits non-trivial 4-quasiplanar mappings (it is an analog of the theorem of Beltrami in the theory of geodetic mappings of Riemannian spaces). It is shown that the 4-quasiplane semi-quaternion Kahlerian space represents a direct product of two Kahlerian spaces of constant holomorphic curvature.

Keywords:
Riemannian spaces, quaternion structure, Kahlerian structure

##plugins.themes.bootstrap3.article.details##

How to Cite
Kurbatova, I. (2017). On 4-quasiplanar mappings of semi-quaternion manifolds. Proceedings of the International Geometry Center, 9(2). https://doi.org/10.15673/tmgc.v9i2.281
Issue
Vol 9 No 2 (2016)
Section
Papers

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.

Provided they are the owners of the copyright to their work, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository, in a journal or publish it in a book), with an acknowledgment of its initial publication in this journal.

Authors are permitted and encouraged to post their work online (e.g., in institutional repositories, disciplinary repositories, or on their website) prior to and during the submission process.

Author Biography

Irina Kurbatova, Odessa national University named after I. I. Mechnikov

Geometry and topology department, professor of department

References

1. Курбатова И.Н. О 4-квазипланарных отображениях почти кватернионных многообразий // Известия ВУЗов. Математика .1986. No. 1. С. 75-78.

2. Курбатова И.Н. О диффеоморфизмах почти кватернионных многообразий // Мат.Студії. - 2013. - Т.40, No. 1.- С. 95-103.

3. Курбатова И.Н. 4-квазипланарные отображения почти кватернионных и полукватернионных многообразий//Труды международного геометрического центра. – 2015. – Том 8, No. 1.- С.63-73.

4. Д. В. Беклемишев. Дифференциальная геометрия пространств с почти комплексной структурой // Итоги науки: Геометрия, 1963. М.: ВИНИТИ.{1965} 165--212.

5. Синюков Н.С. Геодезические отображения римановых пространств //М.: Наука, Москва, 1979. 256 с.

6. Otsuki, T.; Tashiro, Y. On curves in Kaehlerian spaces. J.Okayama Univ. 4, 57-78 (1954).

7. J.Mikes, A.Vanzurova, I.Hinterleitner. Geodesic Mappings and Some Generalizations//Palacky University, Olomouc, Faculty of Science. Olomouc, 2009.