scholarly journals CR Submanifolds of the Nearly Kähler $$\mathbb {S}^3\times \mathbb {S}^3$$ S 3 × S 3 Characterised by Properties of the Almost Product Structure

2018 ◽  
Vol 15 (3) ◽  
Author(s):  
Miroslava Antić ◽  
Nataša Djurdjević ◽  
Marilena Moruz
Keyword(s):  
Product Structure ◽  
Almost Product Structure ◽  
Nearly Kähler ◽  
Cr Submanifolds

scholarly journals Properties of the nearly kähler S3×S3

2018 ◽  
Vol 103 (117) ◽  
pp. 147-158 ◽  
Author(s):  
Marilena Moruz ◽  
Luc Vrancken
Keyword(s):  
Complex Structure ◽  
Product Structure ◽  
Almost Complex Structure ◽  
Almost Product Structure ◽  
Almost Complex ◽  
Nearly Kähler

We show how the metric, the almost complex structure and the almost product structure of the homogeneous nearly Kahler S3 ? S3 can be recovered from a submersion ? : S3 ? S3 ? S3 ? S3 ? S3. On S3 ? S3 ? S3 we have the maps obtained either by changing two coordinates, or by cyclic permutations. We show that these maps project to maps from S3 ? S3 to S3 ? S3 and we investigate their behavior.

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.

Note on Almost Product Manifolds and their Tangent Bundles

1966 ◽  
Vol 9 (05) ◽  
pp. 621-630
Author(s):  
Chorng Shi Houh
Keyword(s):  
Tangent Bundle ◽  
Tangent Vector ◽  
Product Structure ◽  
Dimensional Manifold ◽  
Almost Product Structure ◽  
Local Coordinates ◽  
Natural Frame ◽  
Class C ◽  
Tangent Bundles ◽  
Differentiability Class

Let Mn be an n-dimensional manifold of differentiability class C∞ with an almost product structure . Let have eigenvalue +1 of multiplicity p and eigenvalue -1 of multiplicity q where p+q = n and p≧1, q≧1. Let T(Mn) be the tangent bundle of M. T(Mn) is a 2n dimensional manifold of class C∞. Let xi be the local coordinates of a point P of Mn. The local coordinates of T(Mn) can be expressed by 2n variables (xi, yi) where xi are coordinates of the point P and yi are components of a tangent vector at P with respect to the natural frame constituted by the vectior ∂/∂xi at P.

scholarly journals The Geometry of Product Conjugate Connections

2013 ◽  
Vol 59 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Adara M. Blaga ◽  
Mircea Crăşmăreanu
Keyword(s):  
Product Structure ◽  
Tensor Fields ◽  
Almost Product Structure ◽  
Conjugate Connections ◽  
Hermitian Geometry ◽  
The Given

Abstract Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of these tensors. Some examples from the geometry of a pair of complementary distributions are discussed and for this case the above structural and virtual tensors are expressed in terms of O’Neill-Gray tensor fields.

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.

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