scholarly journals Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ntokozo Sibonelo Khuzwayo ◽  
Fortuné Massamba
Keyword(s):  
Vector Field ◽  
Curvature Vector ◽  
Almost Kähler Manifold ◽  
Canonical Foliation ◽  
Almost Kähler ◽  
The Mean ◽  
Curvature Tensors ◽  
Locally Conformal ◽  
Kähler Structures ◽  
Almost Kähler Structures

We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.

scholarly journals Pseudo-Reimannian manifolds endowed with an almost paraf-structure

1985 ◽  
Vol 8 (2) ◽  
pp. 257-266 ◽  
Author(s):  
Vladislav V. Goldberg ◽  
Radu Rosca
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Mean Curvature ◽  
Integral Manifold ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Minimal Hypersurfaces ◽  
Reimannian Manifolds ◽  
The Mean ◽  
Orthogonal Distribution

LetM˜(U,Ω˜,η˜,ξ,g˜)be a pseudo-Riemannian manifold of signature(n+1,n). One defines onM˜an almost cosymplectic paraf-structure and proves that a manifoldM˜endowed with such a structure isξ-Ricci flat and is foliated by minimal hypersurfaces normal toξ, which are of Otsuki's type. Further one considers onM˜a2(n−1)-dimensional involutive distributionP⊥and a recurrent vector fieldV˜. It is proved that the maximal integral manifoldM⊥ofP⊥hasVas the mean curvature vector (up to1/2(n−1)). If the complimentary orthogonal distributionPofP⊥is also involutive, then the whole manifoldM˜is foliate. Different other properties regarding the vector fieldV˜are discussed.

The k-almost Yamabe solitons and almost coKähler manifolds

2021 ◽  
pp. 2150179
Author(s):  
Xiaomin Chen ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Riemannian Product ◽  
Reeb Vector ◽  
Potential Vector ◽  
Reeb Vector Field ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Yamabe Solitons ◽  
Potential Vector Field

In this paper, we study almost coKähler manifolds admitting [Formula: see text]-almost Yamabe solitons [Formula: see text]. First, we obtain a classification of almost coKähler [Formula: see text]-manifolds admitting nontrivial closed [Formula: see text]-almost Yamabe solitons. Next, we consider an almost [Formula: see text]-coKähler manifold admitting a nontrivial [Formula: see text]-almost Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector field. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector field, we also obtain two results.

scholarly journals On cohomological decomposability of almost–Kähler structures

2014 ◽  
Vol 142 (10) ◽  
pp. 3615-3630 ◽  
Author(s):  
Daniele Angella ◽  
Adriano Tomassini ◽  
Weiyi Zhang
Keyword(s):  
Almost Kähler ◽  
Kähler Structures ◽  
Almost Kähler Structures

scholarly journals On the uniqueness of almost-Kähler structures

2010 ◽  
Vol 348 (7-8) ◽  
pp. 423-425
Author(s):  
Antonio J. di Scala ◽  
Paul-Andi Nagy
Keyword(s):  
Almost Kähler ◽  
Kähler Structures ◽  
Almost Kähler Structures

scholarly journals Some critical almost Kähler structures

2008 ◽  
Vol 111 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Takashi Oguro ◽  
Kouei Sekigawa
Keyword(s):  
Almost Kähler ◽  
Kähler Structures ◽  
Almost Kähler Structures

SURFACES IN Sn WITH PRESCRIBED GAUSS MAP AND MEAN CURVATURE VECTOR FIELD

2006 ◽  
Vol 17 (10) ◽  
pp. 1127-1143
Author(s):  
AYAKO TANAKA
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Sufficient Conditions ◽  
Curvature Vector ◽  
Gauss Map ◽  
Necessary And Sufficient Conditions ◽  
Mean Curvature Vector ◽  
The Mean ◽  
Necessary And Sufficient

We give relations between the Gauss map and the mean curvature vector field of a surface in the Euclidean unit n-sphere Sn. These relations are necessary and sufficient conditions for the existence of a surface in Sn with prescribed Gauss map and mean curvature vector field. We show that such surfaces can be expressed explicitly by using given data.

Almost quasi-Yamabe solitons on almost cosymplectic manifolds

2020 ◽  
Vol 17 (05) ◽  
pp. 2050070
Author(s):  
Xiaomin Chen
Keyword(s):  
Vector Field ◽  
Riemannian Product ◽  
Reeb Vector ◽  
Potential Vector ◽  
Cosymplectic Manifolds ◽  
Almost Kähler Manifold ◽  
Almost Kähler ◽  
Yamabe Solitons ◽  
Yamabe Soliton ◽  
Potential Vector Field

In this paper, we study almost cosymplectic manifolds admitting almost quasi-Yamabe solitons [Formula: see text]. First, we prove that an almost cosymplectic [Formula: see text]-manifold is locally isomorphic to a Lie group if [Formula: see text] is a nontrivial closed quasi-Yamabe soliton. Next, we consider an almost [Formula: see text]-cosymplectic manifold admitting a nontrivial almost quasi-Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector filed. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector filed, we also obtain two results. Finally, for a closed almost quasi-Yamabe soliton on compact [Formula: see text]-cosymplectic manifolds, we prove that it is trivial if [Formula: see text] is nonnegative, where [Formula: see text] is the scalar curvature.

Sign in / Sign up

Export Citation Format

Share Document