A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds
M Antić - Mathematica Slovaca, 2018 - degruyter.com
Mathematica Slovaca, 2018•degruyter.com
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 …
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 …
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 , 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 coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.