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

Year, pages: 2018, 1129 - 1140

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 $\S^6(1)$, 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 $\S^3$ coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.

Antić, M. 2018. A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds. In Mathematica Slovaca, vol. 68, no.5, pp. 1129-1140. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0175

Antić, M. (2018). A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds. Mathematica Slovaca, 68(5), 1129-1140. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0175