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

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

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.

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.

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.

The umbilical locus on the boundary of strictly pseudoconvex domains in ℂ2

2017 ◽  
Vol 28 (09) ◽  
pp. 1740001
Author(s):  
Peter Ebenfelt
Keyword(s):  
Three Dimensional ◽  
Pseudoconvex Domains ◽  
Umbilical Points ◽  
Cr Submanifolds

The main objective of this paper is to survey some recent results on the Chern–Moser question concerning existence of umbilical points on three-dimensional CR submanifolds in [Formula: see text].

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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