Three-dimensional CR submanifolds of the nearly Kähler $$\mathbb {S}^3\times \mathbb {S}^3$$ S 3 × S 3

2018 ◽  
Vol 198 (1) ◽  
pp. 227-242 ◽  
Author(s):  
Miroslava Antić ◽  
Nataša Djurdjević ◽  
Marilena Moruz ◽  
Luc Vrancken
Keyword(s):  
Three Dimensional ◽  
Nearly Kähler ◽  
Cr Submanifolds

scholarly journals Ruled three-dimensional CR submanifolds of the sphere S6(1)

2017 ◽  
Vol 101 (115) ◽  
pp. 25-35 ◽  
Author(s):  
Miroslava Antic
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Totally Geodesic ◽  
Geodesic Spheres ◽  
Nearly Kähler ◽  
Cr Submanifolds

We investigate proper, three-dimensional CR submanifolds of the nearly Kahler sphere S6(1) ruled by totally geodesic spheres S2(1), and classify them by using a sphere curve and a vector field along that curve.

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

2018 ◽  
Vol 68 (5) ◽  
pp. 1129-1140
Author(s):  
Miroslava Antić
Keyword(s):  
Three Dimensional ◽  
Kähler Manifolds ◽  
Moving Frame ◽  
Kahler Manifolds ◽  
Twisted Product ◽  
Totally Geodesic ◽  
Cr Structure ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds ◽  
Cr Submanifolds

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 $ \mathbb{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 $ \mathbb{S}^{3} $ coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.

THREE-DIMENSIONAL CR-SUBMANIFOLDS IN THE NEARLY KÄHLER 6-SPHERE WITH ONE-DIMENSIONAL NULLITY

2009 ◽  
Vol 20 (02) ◽  
pp. 189-208 ◽  
Author(s):  
MIRJANA DJORIĆ ◽  
LUC VRANCKEN
Keyword(s):  
Three Dimensional ◽  
Dimensional Sphere ◽  
Totally Geodesic ◽  
One Dimensional ◽  
3 Dimensional ◽  
Totally Geodesic Submanifolds ◽  
Nearly Kähler ◽  
Nullity Distribution ◽  
Cr Submanifolds

In this paper, we study certain three-dimensional CR-submanifolds M of the nearly Kähler 6-dimensional sphere S6(1). It is well known that there does not exist a three-dimensional totally geodesic proper CR-submanifold in S6(1). In this paper we obtain a classification of the 3-dimensional CR-submanifolds which are the closest possible to totally geodesic submanifolds, i.e. those that admit a one-dimensional nullity distribution.

Three-dimensional minimal CR submanifolds in satisfying Chen’s equality

2006 ◽  
Vol 56 (11) ◽  
pp. 2279-2288 ◽  
Author(s):  
Mirjana Djorić ◽  
Luc Vrancken
Keyword(s):  
Three Dimensional ◽  
Cr Submanifolds

scholarly journals Three-dimensional CR-submanifolds in the nearly Kaehler six-sphere satisfying B.Y. Chen's basic equality

2000 ◽  
Vol 31 (4) ◽  
pp. 289-296
Author(s):  
Tooru Sasahara
Keyword(s):  
Mean Curvature ◽  
Three Dimensional ◽  
Real Space ◽  
Sharp Inequality ◽  
Space Forms ◽  
Equality Case ◽  
3 Dimensional ◽  
Real Space Forms ◽  
Basic Equality ◽  
Cr Submanifolds

B. Y. Chen introduced in [3] an important Riemannian invariant for a Riemannian manifold and obtained a sharp inequality between his invariant and the squared mean curvature for arbitrary submanifolds in real space forms. In this paper we investigate 3-dimensional CR-submanifolds in the nearly Kaehler 6-sphere which realize the equality case of the inequality.

scholarly journals Three-Dimensional Minimal CR Submanifolds of the Sphere S 6 (1) Contained in a Hyperplane

2015 ◽  
Vol 12 (4) ◽  
pp. 1429-1449 ◽  
Author(s):  
Miroslava Antić ◽  
Luc Vrancken
Keyword(s):  
Three Dimensional ◽  
Cr Submanifolds
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