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Mathematica Slovaca

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Volume 68, Issue 5

Issues

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

Miroslava Antić
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0175

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 S6(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 S3 coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.

MSC 2010: 53B25; 53C42; 53C25

Keywords: CR submanifold; nearly Kähler manifold; doubly twisted product; ruled submanifolds

This research was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, project 174012.

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About the article

Received: 2017-05-22

Accepted: 2017-09-22

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Július Korbaš


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1129–1140, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0175.

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